A character's unarmed strike is always considered to be two size categories smaller than the character.
Therefore, a medium character is using a tiny weapon to attempt the disarm. This makes Monks really really bad at disarming. A house rule suggested in S&F is to allow Monks to make a two handed disarm attempt, which would make their unarmed attack be treated as if it were the character's size category instead.
As to wether or not you can grab a dis-armed weapon with your off-hand, I would probably allow it. I don't think any official rules cover it, but I do seem to recall there being something about it in Song and Silence.
Hope that helps.