I haven't played much HU. So just generally looking for some pointers.

Hand 1
This villain had been three betting me a lot preflop and calling by 3-bets about 40-50%. This is his first 4-bet.
PokerStars No-Limit Hold'em, $0.50 BB (2 handed) Poker-Stars Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

Hero ($168.05)
Button ($50.75)

Preflop: Hero is BB with Q, A.
Button raises to $2, Hero raises to $6, Button raises to $16, Hero?

Hand 2
Same villain. Called the 3-bet as I was getting a little sick - not the right thing to do I know. Turn push ok?

PokerStars No-Limit Hold'em, $0.50 BB (2 handed) Poker-Stars Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

Hero ($81.60)
BB ($102.90)

Preflop: Hero is Button with T, K.
Hero raises to $2, BB raises to $8, Hero calls $6.

Flop: ($16) 9, 5, Q (2 players)
BB bets $10.5, Hero calls $10.50.

Turn: ($37) K (2 players)
BB bets $12, Hero raises to $32 and calls a push?