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Xp is split between the entire party generally. This helps some characters like bards or battle field controller wizards gain XP while the fighter/ranger/paladin/barbarian kills the enemy. If the character participated in the battle they should get an equal amount of XP.
That said if a player ended up separated and had to solo an encounter and still won then that player should get all XP as he was the only participant.
If you choose to award "quest XP" at the end of a dungeon then it should also be split evenly between the group. The only way a character gets more XP than another is through fighting an encounter alone (or in a smaller group without someone else) a few artifacts (The Deck of Many Things) or some DMs offer roleplaying experience where a player gains bonus XP by roleplaying the character well though that is an optional method that is not by the rules as far as I know.
I hope this helps, and welcome to RPGs.
One small thing as well about experience: it represents the learning of the player characters. This means that death of the ennemy is not actually mandatory to get the experience points from the encounter. If an ennemy ends up being subdued, or routed out of the combat, he was technically defeated. I do advise to consider these ennemies as well in the count of the experience points.
Correct - experience is generally handed out by defeating the enemy. That also includes talking the enemy out of fighting in the first place, or bypassing the conflict by other cunning means.
XP from traps are also granted whatever the way you used to pass it, even if the only thing you did is walking in it (activating the trap) without knowing there were a trap in the first place.
Going a step beyond, you can drop the XP tracking altogether and level the characters when you think they are ready. makes bookkeeping easier.
This approach has been pretty standard in my games for about 15 years or so ...... WAY easier......
You should make sure to award XP if the characters use diplomacy or intimidation to turn a hostile NPC friendly (or submissive), knock out an NPC but do not kill it, use nonlethal means to capture it, or stealthily sneak around it and completely avoid it. (The last should be a situation where the party is aware of the NPC and actively takes steps to avoid it, as opposed to where they make successful stealth rolls and the NPC never pokes its head out of its lair, and they bypass it without succeeding on a perception check to notice it as well.)