Do monsters have to be behind objects to get a surprise round?
No. They have to be unobserved or otherwise have an surprise advantage over the characters.
http://paizo.com/prd/combat.html
When a combat starts, if you are not aware of your opponents and they are aware of you, you're surprised.
Likewise it goes on to say
The Surprise Round: If some but not all of the combatants are aware of their opponents, a surprise round happens before regular rounds begin.
In your scenario you state:
"If I have a monster on either side of the entrance, back a few squares,they [the creatures?] are unperceived until the players enter at which time the creatures would want to strike."
It seems that you mean the monsters are unperceived by the party while the adventurers are being very observable, making lots of noise and carrying a light source prior to entering the room. If the party isn't being actively observant, these conditions should grant the monsters an automatic surprise round against the party, assuming the creatures have any chance of being in a position to attack the characters when the party enters.
Perception vs. Stealth should only come into play before entering the room (e.g. somewhere along the hallway).
If the monsters are observable before the party enters the room (the adventurers hear shuffling/snorting, the creatures give off a fetid stench, magical detection, active party awareness, etc.), this could warrant a check to stay hidden.
http://www.d20pfsrd.com/skills/stealth
You are skilled at avoiding detection, allowing you to slip past foes or strike from an unseen position. This skill covers hiding and moving silently. [emphasis added]
This is where the Perception vs. Stealth check should be utilized. Unless the party is peeking around every corner with a mirror prior to entering (or has other ways of detecting the creatures), the advantage most likely goes to the prepped monsters for line of sight (thus being "unseen") -- if nothing else.
If you have a monster on either side of the door, whichever direction the first character looks will obscure the other monster. If you have a monster rushing a foe with a light, you can argue it's blinded by the light (negating surprise), but barring this, it is much easier for the creature to pinpoint the torchbearer than vice-verse. You also specified a square room, meaning that, side to side, directly left or right and closest to the door, only a length of perhaps 5' - 10' (one to two 5' squares) would be visible to the player(s) entering until both a light and head/half the full body of the first adventurer(s) were through the door.
Again, the creature(s) be should along the walls closest to the door. Standing away from the wall would likely move the creatures into a character's natural cone of vision (line of sight), negating its potential ability to hide (per illumination from a light sources).
If the creatures are clearly out of sight of the party and trying to remain out of sight until all the party members enter the room, you could use Perception vs. Stealth. However, it might be wise to ask yourself how the creatures know how many party members there are.
Your Stealth check is opposed by the Perception check of anyone who might notice you. [emphasis added]
As I am not aware of any rules stating a Perception vs. Stealth is required to enter a surprise round and it is pretty clear Stealth assumes some sort of active giveaway, Perception vs. Stealth may not even be appropriate to utilize at all.
As for who gets to act, the characters behind the player(s) entering the room would almost certainly get no actions in the surprise round.
Combatants who are unaware at the start of battle don't get to act in the surprise round.
Assuming they cannot see or sense the creature(s) in waiting (Perception vs. Stealth if appropriate), then they have essentially no chance of acting. The characters entering through the doorway should be able to act in the surprise round, assuming they are not surprised (perceived the monsters prior to room entry).
EDIT
"Should I mentally be telling myself the 2 monsters have readied a charge action on somebody coming through that door?"
Yes. Pre-planning any attack never hurts. You should be aware of any special circumstances or restrictions on your proposed tactics ahead of time. For instance, if you follow the rules as written, Charging has special restrictions during a surprise round.
http://paizo.com/prd/combat.html
Suprise
In initiative order (highest to lowest), combatants who started the battle aware of their opponents each take a standard or move action during the surprise round. [emphasis added]
Charging
Charging is a special full-round action that allows you to move up to twice your speed and attack during the action. [...] If you are able to take only a standard action on your turn, you can still charge, but you are only allowed to move up to your speed (instead of up to double your speed) and you cannot draw a weapon unless you possess the Quick Draw feat. You can't use this option unless you are restricted to taking only a standard action on your turn. [emphasis added]
Charging has other general restrictions including a minimum of 10' of movement, limiting attackers to a single melee attack (even if they are capable of multiple attacks) and having a clear path to an opponent. So it is an extremely good idea to evaluate your monsters' strategies ahead of time.
As a rule of thumb, I would feel comfortable in utilizing any attack that the creature would normally use, barring some special powers. A slime dropping on an opponent is not a special attack - it's how slimes hunt. Genuinely special attacks would not top my list of attacks to use except under exceptional circumstance. For example, a dragon, no matter how paranoid, would probably be unlikely to use a breath weapon immediately - they are almost certainly too smug about their general superiority. An exception could be made, however, if the dragon had recently been the target of another credible attack.
Regarding character awareness:
What if the player claims that their characters should not be surprised because they are in a dungeon and are expecting a monster in every room. Thus they would enter each room ready for a fight. Does this make any impact?
From a pure rules standpoint, it makes no difference whatsoever. Characters can always be surprised unless there is another rule stating that they cannot (such as from a magical item or effect). At the very least, every player has the possibility (in most cases) of failing a roll, especially if penalties are applied.
If you wish to concede that the party is always on their tiptoes and allow players a Perception check prior to entering every room with hidden opponents, this may appease some players, but not all. Inevitably, they will fail a roll at some point and be surprised.
Perception is for observation, Investigation is for deduction.
Some of this answer will be observations on how Wizards has done it so far and some of this will be logic, and some of it will be mechanics.
First for the headline question. It depends. when to use Investigation, and when to use Perception is not entirely clear yet, and I'm hoping we'll get more guidance in the DMG late this year. The guidance from the rules is that the two skills mostly seem to differ in the methods by which they are found.
Depending on the exercise, either, or both of the skills may be used.
For passive checks, you're almost always looking at Perception being the skill of record. While all skills can be used passively, some skills make more sense than others. Perception is the hallmark passive skill, whereas investigation makes less sense as a passive skill.
If the character is alert to the possibility of hidden objects/traps, but not actively searching, he's using passive perception.
The guidance for this seems to be (though we can't confirm yet), that the DC for actively looking for something is regularly about 5 less than the DC for passively looking for something (or sometimes actively looking always reveals it).
So here's how I would play it. Traps can be noticed with perception passively (usually DC 15). If the PC is looking, ask them how they are looking. If it's observational, then use Perception. If it's deductive, use Investigation. When they are searching for items, again, either skill is appropriate. This is somewhat counter to how WOTC has written adventures so far. They are always written to use perception to notice traps. Passive with a higher DC and active with a lower.
Investigation also has broader uses such as when you are trying to track clues, or put something together. It's also a great "roll for a hint" kind of skill if your PCs get stuck and need some help figuring out what to do next.
Best Answer
RAW the Rogue does receive the benefits of Expertise to his passive.
The player has invested in making this character good at this, this is not a bad thing.
Rogues in general are supposed to be good at this type of thing, hence the proficiency bonus class feature and the player specifically spent a feat on making his passive perception better. The player could've spent this on another feat to specialize in another area (or gain a combat ability). This is a good thing, while it may make it difficult for the Rogue to be surprised by a trap or an ambush you should in no way try to outmaneuver this.
Don't worry, there are downsides to the Rogue for this.
To reliably spot traps and ambushes the rogue will need to be at the head of the marching order so that he has clear sight lines. Rogue's are not particularly hardy and the party as a whole is inviting more risk for this reward. Likewise while he is extremely excellent at spotting physical dangers, the Rogue will not be able to detect magic wards and other dangerous enchantments and may equally blunder into them.
Ways to handle his detection of a trap or an ambush
You are correct in assuming that only that PC has seen the trap/enemy. Unless he has some mode of telepathic communication he will need to speak out and announce the threat to everyone. The best way to handle this sort of thing is to pass notes or send text messages to the player(s) able to see/detect the issue and leave it to them to react and tell someone else. Intelligent enemies will see/hear the rogue warning the party and the combat should start immediately (no surprise round though).
The PC does not become omniscient of the trap upon detecting it.
The PHB itself is very, very vague on what information is received when a PC detects a trap. However, the DMG does have a nice little section about traps, their detection, and disarming them:
Essentially though whether trap disarming is simply a dex check, a series of checks, and/or involves serious RP is up to you as a DM. I would encourage the open-ended approach the book suggests as it adds complexity and makes trap checking and disarming a more engaging process. Sitdown with the party OOC and discuss what the table as a whole thinks should happen for trap checks and move forward based on that consensus.