Hand 1:

After the villain checks the flop, what is the correct play on the turn? Im pretty clueless here given that I dont really have any reads...

PokerStars No-Limit Hold'em, $0.05 BB (4 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

Hero (SB) ($9.48)
BB ($6.06)
UTG ($5.01)
Button ($11.79)

Preflop: Hero is SB with 7, 7
1 fold, Button raises to $0.20, Hero calls $0.18, 1 fold

Flop: ($0.45) 4, K, 2 (2 players)
Hero checks, Button checks

Turn: ($0.45) 10 (2 players)
Hero bets $0.40, Button calls $0.40

River: ($1.25) 6 (2 players)
Hero checks, Button bets $0.90, Hero folds

Total pot: $1.25 | Rake: $0.05

Hand 2:

Preflop I dont see the villain just min raising with AT+ so on the flop Im pretty sure that I am ahead. At the same time I want to control the pot size with only TPNK. Should I be looking to raise on any of the streets?

PokerStars No-Limit Hold'em, $0.05 BB (6 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

BB ($5.86)
UTG ($4.72)
MP ($11.46)
CO ($5.56)
Button ($4.39)
Hero (SB) ($8.66)

Preflop: Hero is SB with A, 9
UTG calls $0.05, 3 folds, Hero calls $0.03, BB raises to $0.10, UTG calls $0.05, Hero calls $0.05

Flop: ($0.30) K, 2, A (3 players)
Hero checks, BB bets $0.15, 1 fold, Hero calls $0.15

Turn: ($0.60) 4 (2 players)
Hero checks, BB bets $0.25, Hero calls $0.25

River: ($1.10) Q (2 players)
Hero checks, BB checks

Total pot: $1.10 | Rake: $0.05