Roles Can Be A Bummer
Making actions/options not available to people can force people out of the magic circle pretty quickly. Sure, roles can help people feel special, but it can go overboard. This does not mean that the rogue shouldn't be stealthy, or that the cleric can't be tank-y, but not being able to use or do something because of an arbitrary class restriction breaks the circle, which means less fun for everyone.
Sometimes, multiple people actually can do the same thing, and that should happen sometimes. If every task you throw at the player characters cannot be accomplished except for 1 person's specialization, it may be a harder adventure than these players (as a group) are fit for. Not that there can't be a situation where you need a particular player to do a something, but that it shouldn't happen all the time.
Perhaps It is a Matter of Perception
So maybe this player is simply just does not imagine the same thing you do. You can try to reinforce what you envision by describing what is going on. Is she/he making informed choices? Does she/he realize what the gravity of the situation, or how her/his character has certain strengths?
Does this player realize the cleric is running around in thick armor, while that player's character is running around in normal clothes? For example, if I think the cleric is running around in normal clothes, and goes into combat and comes out unscathed, I could run in my normal clothes, and also come out unscathed.
If this is the problem, you simply need to be more descriptive! Describe how the cleric is wearing armor, or how the rogue is especially cat-like, and how this player's character is not.
For Games Which Depend On Roles
It may be time to have your other players step up. Have the cleric yell at the other character to stay back, or that the cleric "has this." Alternatively, the cleric may ask "PEASE SUMMON THIS TO HELP ME!" as he charges in.
If the rogue attempts to sneak around, the rogue can give specific instructions; "Can you make a distraction over there?" "Wait here, and if I'm not back in 15 minutes, go get the others to rescue me." Or even: "this looks super dangerous. I don't think you'll make it. We don't want to get ourselves killed, yeah?"
In short, give him tasks, or have the other players give him tasks to help with things. Talking is a free action in combat; use it. This is especially good for players who may be experiencing some mental handicap; it gives them something concrete to act on. It allows them to contribute (which feels great and is fun) without going through negative experiences.
Finally, a player or the DM can specifically highlight when certain actions will require a specific specialization, and who has that training. If it becomes obvious that a task is dangerous and requires training, then most people leave it to the person with the training. The DM can further forbid people without specialization from trying, stating that it's obviously too hard. This is more "hand-holdy" than some people like it, but sometimes people just need their hands held.
Talk About It
Talk with the player about the roles. What is her/his character good at? What should she/he focus on? These other characters have something special about them, what is she/he special at?
Talk about how their character is so good at magic/whatever else, and how they should try to make their magic/whatever else be the solution for the current situation. (After all, we're solving these situations using our strengths, use your strengths to help solve it!)
Tough Love
Finally, you may have to resort to letting the consequences of this player's action happen. Let the events, despite other character's best efforts, happen. Talk about how that character was not focusing on what they were good at, or how their play-style does not match up well with the class they chose. Make a new character that does okay at everything, such as most games' version of a "bard." Note: this does not mean make a character who is rule-breaking and superior to all the others, but one that stands a decent chance at performing many things, and isn't a large risk to the success of most tasks.
This isn't a rules problem, it's a diva problem.
A player who wants the attention of the game focused on him and his awesomeness - by using attacks that let him dominate the battlefield and prevent other players from participating, or by getting upset and hogging your attention (via arguing about the rules) when he can't do so - is a diva, and needs to be handled as such.
Before doing anything, though, you need to determine how much his spotlight-hogging is bothering the other players. Do they get frustrated when he dominates combat and prevents them from joining in? Or are they happy to sit back and let him kill monsters, while they handle other things?
If everyone except you is generally happy with the status quo, then it's probably best to just let it go, and take that into account when building encounters. Give lots of mooks for the wizard to spam with Chain Lightning during combat, then give the other players spotlight time by including whatever type of scenario they enjoy. Let the wizard have his awesome. (Although if you don't enjoy this, then consider winding down the game and starting a new one that better suits your own style.)
Otherwise, assuming the other players also don't enjoy the wizard's behavior, you have a few options:
Enforce Your DM Authority
You're the DM, and you've already used that authority (however accidentally) to create houserules that benefit the players. Now use your authority to enforce houserules that don't benefit the players. When the wizard complains about a ruling you've made, say, "This game uses a lot of houserules. This is one of those houserules. Because of that, the rule you're citing doesn't apply in this case." As others have suggested, it may help to write down all your houserules explicitly, so that when the wizard tries to argue RAW, you can point to a specific houserule if applicable.
This is a socially tricky option, since it's likely to make the problem player feel punished. However, as long as you're consistent, polite, and firm, any tantrums he throws will reflect badly on him rather than you.
Reset the Rules
You say you have a bunch of houserules that mostly happened because you as a new DM didn't know any better, yet your wizard is trying to fight you with RAW. Explain to your players that keeping track of all your accidental houserules is becoming a problem, especially as the PCs increase in level and the math to balance things gets trickier. Then declare all house rules null and void, and require that play operates strictly on RAW from now on.
This option may be technically tricky, depending on the specific nature of your houserules. It may require reworking characters who've been built around the assumptions in the houserules. You may upset some of your other players who've been benefitting from the power-ups the houserules provide. And you'll almost certainly upset the wizard, who from your description will probably feel like he's being nerfed. However, you can point out - without naming names - that since your group is spending a lot of time during game going over the RAW, making sure all the PCs conform to the RAW will reduce that non-game time and let you spend more time actually playing.
Boot the Wizard
If the wizard's arguing is making the game not fun for you and the other players, but everyone else gets along just fine with each other and your houserules, then it may be best to simply stop playing with him. The easiest way to do this is to speak with the wizard privately. Tell him that you've come to realize that his playstyle is very different than that of the game you're running. Explain that this difference is making the game not fun for you (and if you know that other players don't enjoy his arguing, you can add "and others in the group", but absolutely don't name names). Tell him his character will be dealt with respectfully in game, and (if it's true) say that you'd be happy to game again with him sometime in the future, in a setting more compatible with both your playstyles.
This is another socially tricky option, but if this player is sapping all your game time arguing with you about the rules and hogging the spotlight, then it may be better for everyone to cut him loose.
Nuke the Game and Start Over
This is, well, the nuclear option: wrap up your game (could be as simple as "rocks fall everyone dies", or take a session or two to provide closure), then start a new game that either doesn't use houserules, or which has explicit agreement from all players that houserules will be used, and only minimal game time will be given to debating them (e.g., when dealing with a corner case). You can choose whether or not to invite the wizard back to this new game; if you think he'll continue to argue with you and hog the spotlight, it might be best - for your own sanity - to not continue to game with him.
Best Answer
Make the campaign manage this
At low levels the basic method of detecting magic is through the use of the spell detect magic. At low levels the basic method of determining whether a creature's evil is the paladin's spell-like ability detect evil. The spell detect magic has verbal and somatic components and, when it's cast, provokes attacks of opportunity. Using the spell-like ability detect evil also provokes attacks of opportunity. Both require the user to concentrate to maintain them.
In other words, every time the character casts detect magic, he's actually casting a for-reals spell. Right there. Now. Because they lack the skill Spellcraft, most creatures won't know what spell it is while it's being cast. But most campaigns do assume even a commoner has a passing familiarity with magic: they know it exists or know it when they see it. That means, even if the caster explains what he's doing, friendly creatures will be on edge and less friendly creatures will be wary. However, paranoid creatures will dive under tables, and hostile creatures will seize the opportunity to stab the caster in the face. When a dude starts wiggling fingers and chanting nonsense, he can say he's casting detect magic but the spell could be fireball and the only way most find out the truth is to see what happens when the caster finishes casting the spell. For many creatures, that's like hoping a gun fires candy.
A spell-like ability draws less attention, but it still draws enough attention to provoke attacks of opportunity. Folks nearby know the user is doing something, and because there are no obvious outward signs beyond a 3 second or so window during which the user lets his guard down, that's a really important window. Folks will look for that and will at least ask what he's doing, if not punch him in the kidney just to be safe.
I'm of the opinion that a magic-saturated world would be extremely paranoid about folks casting spells (and, in the same vein, using spell-like abilities). One lone spell can destroy the lives of hundreds of people, leave a community devastated, or reshape the very landscape. A caster can tote a dozen WMDs in his noggin and no one would know! Everyone should be on the lookout for casters. Casters should very carefully explain to onlookers what spells they're casting. Towns should have regulations about casting. Towns should monitor casters. No one—not even a paladin—should be able to, for instance, walk into the mayor's office and, without asking or warning, use a spell-like ability in his presence. That'll earn the paladin a pike in the gut because he just tried to use a spell-like ability on the mayor! The mayor and his guards don't, won't, and can't care that it was only a silly little detect evil when it could've just as well been dominate person or earthquake.
This all assumes an adventure in civilization. In a dungeon, this only matters during negotiations but the same guidelines should apply. Unannounced casting or use of spell-like abilities should cause tempers to flare and negotiations to end.
The character is being paranoid. As an adventurer, he's allowed to be. But is the world being paranoid enough about the character?
Not all evil is EVIL and not all magic is MAGIC
In a world where possibly more than 1/3 of living (and not-so-) creatures are evil and magic is everywhere, being able to detect evil and magic isn't really that big of a deal. A few semi-false positives should be all it takes to curb a leap-before-looking attitude of attacking every creature that shows up as evil or robbing every creature that possesses a magic item.
The GM should keep in mind that being evil isn't the same as being villainous just as being good isn't the same as being virtuous. Pedestrian evil should be everywhere: the shopkeeper who sells dented goods at full price, the miller who underpays local farmers for their grain, and the town guard who'll look the other way for a little coin may all be evil. And while most of that won't show up with detect evil, evil often achieves success on the backs of good and neutral, so it should come as no surprise to PCs that many lower- and mid-level townsfolk—despite not eating babies, worshiping Orcus, or kicking dogs—just so happen to be evil.
Also keep in mind that it usually takes a significant evil for detect evil to register any evil. That is, typical evil creatures that aren't outsiders or undead don't show up on detect evil until they've at least 5 Hit Dice or levels. (Creatures with cleric levels and other classes with the extraordinary ability aura show up earlier than that, though.) But Pathfinder—for good or ill—doesn't provide the same grainy distribution of alignment, levels, and classes that its antecedent D&D 3.5 does. That leaves the GM free to populate towns with as many level-5-or-higher NPCs as the GM desires and make those NPCs evil if the GM wants.
Like making evil more common, I also recommend making magic more common. Even a level 1 commoner's budget can reasonably include a magic item or two. (They prefer potions, but as tzxAzrael recommends, a few very-low-powered custom magic items are great for challenging players' expectations.) Consider also the tendency of folks to have gotten the spell magic aura cast on their stuff—despite its saving throw and duration of days, it's really inexpensive—, whether so they can appear more important or less. (I can imagine a ritzy party where folks paid to have magic aura cast on everything so the place lights up like Warehouse 13 when detect magic is used… just to show off.) Further, longstanding architecture should incorporate a magical convenience or two, perhaps so much that it permeates the grounds. (In campaigns I run, for example, the spell hallow is frequently a feature of important—and sometimes unimportant—buildings and areas. As an aside, secure areas—or areas that were used as secure areas until they changed hands—often incorporate thin sheets of lead to foil the vast majority of detect spells.)
Knowing that there's evil or magic afoot shouldn't destroy any plots if PCs must first determine which evil or magic is really important.