Hand 1:
Fairly new to table. Villain seems loose.

How's my play? Specially turn check?

PokerStars No-Limit Hold'em, $0.02 BB (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

saw flop|saw showdown

Hero ($4.89)
SB ($3.18)
BB ($2.51)
UTG ($1.86)
MP ($2.48)
CO ($4.17)

Preflop: Hero is Button with 2, 2.
1 fold, MP calls $0.02, 1 fold, Hero raises to $0.1, SB calls $0.09, BB calls $0.08, MP folds.

Flop: ($0.32) A, 6, 2 (3 players)
SB bets $0.1, BB folds, Hero raises to $0.3, SB calls $0.20.

Turn: ($0.92) 6 (2 players)
SB checks, Hero checks.

River: ($0.92) T (2 players)
SB bets $0.8, Hero raises to $2, SB calls $1.20.

Final Pot: $4.92

Hand 2:
Over-the top aggression, but I considered they'd fold if they'd just caught a little of the flop and if they had missed they couldn't call on a bluff.
If they'd flopped 2-pair or better, I'd be dead... but thought this would be +EV.

No great read on the villain. But plays short-stacked passively.

Faulty thinking?

PokerStars No-Limit Hold'em, $0.02 BB (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

saw flop|saw showdown

SB ($1.52)
BB ($1.87)
UTG ($1.50)
MP ($2.65)
CO ($1.78)
Hero ($5.67)

Preflop: Hero is Button with 5, 5.
3 folds, Hero raises to $0.08, SB calls $0.07, 1 fold.

Flop: ($0.18) 7, T, J (2 players)
SB checks, Hero bets $0.15, SB raises to $0.3, Hero raises to $2, SB calls $1.14 (All-In).

Final Pot: $3.62