OK so just to let you know on the second hand both players had AA.
The first hand is the one I'm really concerned about. What should i do in situations like this post flop, when I have hands like TPTK and what not? What do I do on the turn when a brick falls, or a scare card? What about the river? When do i stay with the hand and when do I let it go?
Here's a simular type of hand.

PokerStars No-Limit Hold'em, $0.25 BB (8 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

BB ($13.15)
UTG ($42.40)
UTG+1 ($24.40)
MP1 ($18.90)
Hero ($25.10)
CO ($28.15)
Button ($27.45)
SB ($20.20)

Preflop: Hero is MP2 with J, K.
2 folds, MP1 calls $0.25, Hero raises to $1, 3 folds, BB calls $0.75, MP1 folds.

Flop: ($2.35) K, Q, T (2 players)
BB checks, Hero bets $2, BB calls $2.

Turn: ($6.35) 6 (2 players)
BB checks, Hero bets $4.5, BB calls $4.50.

River: ($15.35) 3 (2 players)
BB checks, Hero bets $5, BB raises to $5.65, Hero calls $0.65.

Final Pot: $26.65