Playing top set against potential flush

Global Poker - $0.05/$0.1 - Holdem - 6 Players

Hero (BB): 15.87 (158.70BB)
UTG: 15.52 (115.20BB)
MP: 19.74 (197.4BB)
CO: 2.03 (20.30BB)
BTN: 14.41 (144.10BB)
SB: 8.50 (85.00BB)

SB posts $0.05, Hero posts BB $0.10, Global Poker puts $0.50 in pot for some reason (some kind of bonus?)

Pre-Flop: (pot: $0.65) Hero has QcQs

UTG raises to $0.50
MP and CO call
SB folds
Hero 3b to $3.05
UTG folds
MP calls
CO calls (all-in $2.03)

Flop: (pot: $9.18) Qd 10d 9h
Hero bets $4.59
MP calls

Turn: (pot: $18.36) Ad
Hero ???

Some questions:

• Is the squeeze sizing of 4/3 pot large enough given hero is out of position?
  
• Is the cbet sizing correct given the flop? With 2 others to act, should I be trying to get more protection?
  
• With Ad on the turn, should hero check or shove? Hero has just under half pot in stack.