Should I have checked behind on the river? I thought he was maybe looking for me to bet whilst holding a set??

PokerStars No-Limit Hold'em, $0.10 BB (6 handed) Poker-Stars Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

MP ($18.70)
CO ($10.05)
Button ($15.15)
SB ($13)
BB ($13.70)
Hero ($20.85)

Preflop: Hero is UTG with A, K.
Hero raises to $0.4, 4 folds, BB calls $0.30.

Flop: ($0.85) 6, 4, 2 (2 players)
BB checks, Hero bets $0.7, BB calls $0.70.

Turn: ($2.25) A (2 players)
BB checks, Hero bets $1.4, BB calls $1.40.

River: ($5.05) T (2 players)
BB checks, Hero checks.

Final Pot: $5.05

Results in white below:
BB has 9s As (one pair, aces).
Hero has Ah Kh (one pair, aces).
Outcome: Hero wins $5.05.

Hand 2: Is my turn on the call bad, and as played, is the river a call or raise?

PokerStars No-Limit Hold'em, $0.10 BB (6 handed) Poker-Stars Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver Cards)

MP ($18.10)
Hero ($11.35)
Button ($1.95)
SB ($9.95)
BB ($9.85)
UTG ($18.05)

Preflop: Hero is CO with , .
1 fold, MP raises to $0.2, Hero raises to $0.8, 3 folds, MP calls $0.60.

Flop: ($1.75) , , (2 players)
MP bets $0.4, Hero calls $0.40.

Turn: ($2.55) (2 players)
MP bets $1.8, Hero calls $1.80.

River: ($6.15) (2 players)
MP bets $0.3, Hero calls $0.30.

Final Pot: $6.75

Results in white below:
MP has 6c Ad (high card, ace).
Hero has Qs Qd (flush, king high).
Outcome: Hero wins $6.75.

Thanks guys.