How do the Kobolds remember which parts are trapped?
Basically, this answer is about weaving the Kobold's own marking system into the narrative. It does assume you draw your own maps and don't use Dungeon Tiles or anything.
Obtain 6 or so pretty looking symbols (they don't need to have meaning, but if they look Draconic it's bonus awesome) Mark every square of the map with one of them. In the narrative, explain that the Kobolds did just that; they covered all the floors with all sorts of markings. For each room, assign 2 symbols to mean "trap" and the others to do nothing. Vary the symbols per room.
This will clearly signal to the players "this room is trapped", but then the word Kobold is basically a synonym for "traps" anyway, so that's okay. It will keep your players attention strongly on the traps, they will try to figure it out by watching Kobold movement (which is good! traps exist in the narrative to be interacted with) and will mostly stumble right into a trap in room 2 before they realise that the Kobolds vary which symbols mean trap in every room.
You could even tie a meaning to each symbol (in Draconic) and explain the words to players who speak it, and then have the chosen symbols make sense per room. Since Kobolds employ deadly traps in their home, they need a system to keep down their own losses, and that has to be simply enough to teach to their kids while still being confusing enough that confound and/or kill enemies.
To tie it even stronger into the narrative, include a room that the Kobolds use for training their young (probably one with few or no Kobolds in it, since they know it's less hurtful) where the traps just drop a bucket of water on their heads or launch sticky paper at them.
And maybe in the newest room, the Kobolds haven't had time to place traps yet, but they did place the markings. Your players will be properly trained by this point to move very carefully, figure out the system, and probably be amused when they realise the Kobolds have trained them like Pavlov's dogs to avoid certain squares, even if they don't do anything. (If they are trained so well they never trigger any, make sure they find a scrap of paper later that has instructions on which traps should go where that makes it clear none of them have been installed yet. Remember: if you don't tell them, it doesn't exist.)
(Regarding the last part, I once trapped my players in a room inside the Temple of the God of Theater, by giving them a huge grid full of letters whose only effect was that certain letters made the floating balls of electricity in the corners light up ominously. They were told that the room was "very dangerous and none had ever traversed it". It took them an hour to figure out they were being played and they loved it.)
What is a trap?
It looks like the crux of your problem is that "trap" is hard to define, particularly with regards to knowledge and time.
After a bit of searching, I found only one location where a trap is actually defined. That's in the Find Traps spell on PHB 241:
A trap, for the purpose of this spell, includes anything that would inflict a sudden or unexpected effect you consider harmful or undesirable, which was specifically intended as such by its creator.
Of course, this is explicitly "for the purpose of [that] spell," so the utility is limited, but it's also the only place where a clear definition for a trap is given.
Based on this definition, a trap is either sudden or unexpected. This means that both of your examples are not traps. They are not sudden, because they have existed for long enough that the PCs can perceive them, and they are not unexpected, because the PCs are aware of them.
Also, if you were to extend the definition of a trap to anything that results from a trap, then this feat could potentially grant resistance to everything in an encounter. For example, a mimic is arguably a trap. Does a dungeon delver get resistance to the mimic throughout the entire fight?
Best Answer
XP is entirely up to the GM
In 5e, the GM can award XP for anything they choose. XP represents experience, and disarming or avoiding a trap is an experience. You don't need guidance on this in RAW, but you could treat it as having the xp value of a monster of a CR equivalent to the PC's average levels, plus or minus 10% depending on how deadly you estimate it to be, if you really need a mechanic.
Personally, I find tracking XP per monster, per encounter, etc extremely fiddly and not worth the effort, and I go for a lump-sum XP award per session, with bonuses for good RP, cool tactics, progress, teamwork, etc. Or use the milestone progression technique and forego XP altogether. Since it's no longer used as a fuel for crafting magic items, like in prior editions, it's not super important as long as your level progression is a reasonable pace.