...just a quick question about the distribution of experience: how the hell is it distributed? Is it split between the characters in your party? Does the "killer" of an enemy get all of it? What about the characters left back in camp? Do they get a share? Is there a difference between "quest experience" and "kill experience", as for example in Baldur's Gate? Is there a level cap?

The DAwiki has a run down for all DA games.
To answer your question,

Experience distribution is full on-screen amount for the character doing the action (killing an enemy, picking a lock, etc.) and 2 experience points less for every other party member. For example, let's say the main character kills a genlock and the experience point gain shown on-screen is 33 XP. That character will have 33 points added to their total and each other party member will get 31 points added.

They don't really gain experience in camp. However, if you have a favorite crew and haven't taken half the people out in a long while, say five levels, you can go somewhere with a party summons and just switch out everyone in order to level them all up occasionally (I like to do this in Redcliffe Village). These characters will be boosted up to within one level of the PC.

Check out the wiki link for more details.
Not quite, you can go into the Character selection while in camp and cycle through your companions. There's a level up button which will be lit up if they've gained a level or more since you last had them in the party.