A 379 [correction] Yes.
Unarmed strikes are natural weapons, which have the unique property of allowing iterative attacks as manufactured weapons do. (Being on the Weapons table just stipulates that it's a weapon, not that it's a manufactured weapon.) Some more extensive quotes from the rules to reinforce Urpriest's point:Originally Posted by Align WeaponOriginally Posted by Magic WeaponOriginally Posted by Magic FangImproved Natural Attack requires a natural weapon, and the Fanged Ring works with unarmed strike as that natural weapon for the granted feat.Originally Posted by Dragon Magic, page 101
The Monk class allows their unarmed strike to also be treated as a manufactured weapon. However, I think it's pretty obvious that an unarmed strike isn't the product of a blacksmith, but rather a natural weapon.
A 380
The Vow of Poverty rules are simple and unyielding.If the character can dispossess themselves of the magic item forced upon them before a single round has expired then they will not break their vow. Wearing any magic item, cursed or not, for a full round will break the vow.You may not, however, “borrow” a cloak of resistance or any other magic item from a companion for even a single round
A 381 Yes.
The Balance check to resist being tripped replaces the usual Dexterity or Strength check. An ability check is always just 1d20 + the appropriate ability modifier, so the size modifier specified in the trip rules is not part of the ability check which you're replacing. Instead, the size modifier is added separately.