TPTK Call on River after LPP Turn C/R?

[grounder]

SB is LPP (47/6/0.95).
BB is LAG (40/21/2.15).

Poker Room skin
Limit Holdem Ring game
Limit: $1/$2
5 players
Converter

Pre-flop: (5 players) Hero is UTG with A Q
<font color="#cc0000">Hero raises</font>, 2 folds, SB calls, <font color="#cc0000">BB 3-bets</font>, <font color="#cc0000">Hero caps</font>, SB calls, BB calls.
I cap figuring that I have enough equity given that SB is LPP.

Flop: 3 A 9 (12SB, 3 players)
SB checks, BB checks, <font color="#cc0000">Hero bets</font>, SB calls, BB calls.
I bet even if BB is planning a c/r with AA/AK because I don't want SB spiking a funky two pair/trips/set.

Turn: 7 (7.5BB, 3 players)
SB checks, BB checks, <font color="#cc0000">Hero bets</font>, <font color="#cc0000">SB raises</font>, BB folds, Hero calls.
SB c/r me on the turn. I'm guessing he has Aces up or a set of 3's or 9s. Plugging it into PokerStove I have 10% against his range. I'm getting 10.5:1 and call.

River: K (11.5BB, 2 players)
<font color="#cc0000">SB bets</font>, Hero ???

1) My AQ is a reverse implied odds hand if SB holds a set. Does this make my turn play a fold?

2) Is this an easy fold on the river even with 12.5:1 (7.4% I need to win) on my call? I don't think he c/r the turn with AT/AJ after a pre-flop cap.

3) If the river was a "Q", giving me top two, do I B/3B, since SB's Aces up contribute more to his range (combination-wise) than a set?