If someone is hiding, do detection attempts always have disadvantage?

This is a great question. From the rules, the answer appears to be 'No', but it isn't explicitly stated. I'm inferring it from this section of the basic rules for Hiding:

Passive Perception. When you hide, there’s a chance someone will notice you even if they aren’t searching. To determine whether such a creature notices you, the DM compares your Dexterity (Stealth) check with that creature’s passive Wisdom (Perception) score, which equals 10 + the creature’s Wisdom modifier, as well as any other bonuses or penalties. If the creature has advantage, add 5. For disadvantage, subtract 5.

For example, if a 1st-level character (with a proficiency bonus of +2) has a Wisdom of 15 (a +2 modifier) and proficiency in Perception, he or she has a passive Wisdom (Perception) of 14.

Emphasis mine. In this case, the rules are specifically explaining how to calculate the passive perception to detect a hidden creature. Since the rules for hidden dictate that the creature must necessarily be unable to be seen clearly (implying light or heavy obscurement), we can infer that this hidden creature is in some way obscured from the searcher. However, since the passive perception total listed is 14, and does not in any way reference a -5 modifier for an obscured creature, it seems like we can be reasonably sure that detecting hidden creatures happens outside the influence of obscurement. Otherwise, the math present would necessarily have to include a -5 for detecting an obscured creature.

Can you sneak up on someone in dim light according to RAW?

This one is DM dependent according to the rules. We can piece this together from the examples that the basic rules give us:

In combat, most creatures stay alert for signs of danger all around, so if you come out of hiding and approach a creature, it usually sees you.

This gives rules for when a creature can detect a hidden creature approaching it. However, since it specifically calls out 'in combat', and since 'out of combat' is not addressed, we have to assume that being out of combat doesn't change the core ruling of the 'hidden' effect (otherwise it would also have a callout, because specific beats general).

The generic hiding rules that necessarily must apply out of combat are:

You can’t hide from a creature that can see you, and if you make noise (such as shouting a warning or knocking over a vase), you give away your position.

and the errata:

The DM decides when circumstances are appropriate for hiding. Also, the question isn’t whether a creature can see you when you’re hiding. The question is whether it can see you clearly.

So in this case, the game is deferring to the DM. You are well within RAW to tell the player that they can't approach the character in dim light from the front and remain hidden. This is even more overt than a simple rule-0, because the published rules specifically call out the DM's ability to overrule it.

My reading of the published rules appear to default to allowing that, but they also give the huge caveat that the DM can overrule it. However, with what we found out above, the detecting creature would NOT receive a -5 penalty by default (unless conditions occurred to warrant disadvantage on the check(s)).

No — you only need to reroll if you do something that the DM determines would expose your location, like make a loud noise or step into clear visibility with no distractions. In that case, if the circumstances allow, you can use your action to hide again. The rules intentionally leave the exact determination up to the DM, but the basic idea is that your one roll covers staying quiet and out of sight over a period of time.

This podcast on the official D&D site has Jeremy Crawford giving about 10 minutes of explanation of stealth. It starts at about 10 minutes in. There is some interesting background detail about the rules in this edition compared to previous edition, and the deliberate design to make the stealth system more up to the DM and less "mechanistic".

The first five minutes really focuses on explaining that in this edition, stealth is by design heavily dependent on the DM's judgment. Then there's a nice explanation of stealth vs perception ­— and specifically that it's normally compared to passive perception.

But it also addresses this particular question specifically, at about 17 minutes in.

Crawford: As soon as the player makes that check, that Dexterity (Stealth) check, they keep that result, whatever the total is, from that check, they keep it until someone discovers them, or they decide to stop hiding. So, this is relevant particularly in combat, because one of the actions you can take in combat on your turn is to hide. You need to spend your whole action doing it. And this rule means, if let's say you want to hide multiple rounds, you don't keep making Dexterity (Stealth) checks round after round — you just make it once. Basically what this means is you only have to spend one action trying to hide, and then once you've done it, you keep whatever that result was, until you're no longer hidden, and again that's either because you've run out of hiding, or you made a loud noise, or someone discovered you. As soon as that happens, even one person discovers you, basically that nullifies whatever you rolled, and if you want to hide again you're going to have to make another check. And what that means in combat, that means you're going to have to spend your action doing that again.

Interviewer: What if for example, though, you hide around a corner of a hallway from somebody, from an enemy that's in the hallway, you get that, so you're hiding around a corner. You're still hidden, but you decide to move, and go into a room as well. Do you still use the initial stealth check, or do you have to roll again when you're moving?

Crawford: Uh, you do not have to roll again.

Interviewer: Interesting!

Crawford: Yeah. The main thing you have to do, once you have made your check, the main thing you have to do to remain hidden is make sure people can't see you clearly, and make sure you're not making a bunch of noise. And, the number that you get from your check really determines how well are you succeeding at those things, how well are you succeeding at staying out of site and staying quiet. And that's ultimately what "hiding" means. [...]

Interviewer: Now, is that rule to speed up play, as far as not making you sure you have to roll a stealth check every round?

Crawford: Yeah, and we in general don't want people to have to make a bunch of rolls for really what is a single process. It's only when basically that process ends, is it time for a new roll.

Interviewer: Got it.

Crawford: And, also, we want you to be able to do other things on your turn, especially when we switch to the combat context. We don't want to make hiding so onerous that it essentially becomes something you never want to do.

Interviewer: Right, that's the only thing you can do on your round.

Crawford: Right, right.

Interviewer: It quickly becomes un-fun.

Crawford: And, there are a number of things that have to stay true for you to remain hidden, once you've made your check. And that again is you have to make sure you're not sort of just standing right out in the open with no visual obstruction at all, and you're not, like, screaming or, you know, shattering things and whatnot.

There's more, but that's the key part relevant here.