Another 3-6 Empire hand - how many bets did I miss?

[binions]

Party Poker 3/6 Hold'em (9 handed) converter

Preflop: Hero is MP1 with 7[img]/images/graemlins/club.gif[/img], 7[img]/images/graemlins/heart.gif[/img].
UTG calls, UTG+1 calls, Hero calls, MP2 calls, <font color="#666666">1 fold</font>, CO calls, <font color="#666666">2 folds</font>, BB checks.

Flop: (6.33 SB) A[img]/images/graemlins/club.gif[/img], 4[img]/images/graemlins/spade.gif[/img], 7[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(6 players)</font>
BB checks, <font color="#CC3333">UTG bets</font>, UTG+1 folds, Hero calls, MP2 calls, <font color="#CC3333">CO raises</font>, BB folds, UTG calls, Hero calls, MP2 calls.

Turn: (7.16 BB) 6[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(4 players)</font>
UTG checks, Hero checks, MP2 checks, <font color="#CC3333">CO bets</font>, UTG calls, <font color="#CC3333">Hero raises</font>, MP2 folds, CO calls, UTG folds.

River: (12.16 BB) Q[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets</font>, CO calls.

Final Pot: 14.16 BB

Questions:

Assuming my preflop call was correct:

1. Should I have raised the flop when it was $3 to me?
2. Should I have re-raised the flop when the cutoff raised on a rainbow board?
3. Should I have checked to the raiser on the turn?
4. Should I have check-raised the turn once the flop raiser bet out?
5. Should I have led out on the river?

Any input is appreciated.