I am wondering if there is a mod that:

1. Will allow me to rest without being interrupted by guards in safe places (like towns).
2. Will not allow me to rest in dangerous places that don't normally allow resting (like the ToB final battle arena)
3. Will not change the situation in dangerous areas that do allow resting (like the wilderness and dungeons)

Also, a mod to allow trading items between party members over arbitrary distances would also be nice.

If you get the Gibberlings 3 Tweak Pack, there is a "rest anywhere' mod that allows you to do just that. There is no guarantee you won't be attacked in dungeons and the wilderness during your sleep, but you can rest indoors in towns with no problems.

The problem, however, is that I don't want it to enable resting in places like the Throne of Bhaal final battle arena, where resting would break the challenge. (Then again, if I ever actually play to that point, I will probably use Wish to regain my spells anyway.)

Couldn't you, just, you know, not rest there? Just because resting is allowed, you aren't obligated to actually do so.

If you have a bag of holding, you could use a saved game editor like IESE to give your companions the same bag of holding & everyone will have access to the same stuff.
Likewise if you have the same potion bag.

Yes, but that assumes I know that resting is not normally allowed there, which assumes familiarity with the game.