#2. i would probably check behing on the turn. it may not be the best line, but that would be my play. there are a lot of draws out there, and he probably isnt going away. we cant be certain we are ahead of him right now, and the 9 completed a possible draw.
#3. if UTG+1 called pf and flop and turn with a 2 in his hand, then i pay him off on the river. if he has a set that filled up, i think he misplayed the hand as your hand is pretty transparent here and he could have probably made some more earlier. other wise you are ahead all the way and should call the river.

#4. i might raise pf. but would almost certainly bet that flop. it isnt often you get an overpair with 77. however, if played back at strongly (esp. by one of the blinds) then i would probably have to let it go.

#5. i expect him to have a large PP here, but still call pf cus he will stack off if you flop something that beats him. on the flop he gives you no odds whatsoever to continue, and i dont think your overcard(s) are clean or even outs.

#6. i would fold pf, but as played i cant fault the flop bet, but after two calls on that board i would probably check the turn, and the fold looks good.

keep in mind i myself am just getting used to cash games, so take the advice for what its worth. if nothing else, at least itll give you something to think about.