Common turn situation tonight, quick check-up

[Genesis]

Ultimate Bet - No Limit Hold'em Cash Game - $0.05/$0.10

Stack sizes assume $10, not very relevant to these situations. Also, only a few hands on each villain, but appear to be loose and fairly passive.

Struggling tonight...Are these the standard lines?

---In Position

Preflop: Hero is dealt T[img]/images/graemlins/club.gif[/img] 8[img]/images/graemlins/spade.gif[/img] (4 Players)
2 folds, SB calls $0.05, Hero checks

Flop: ($0.20) 4[img]/images/graemlins/heart.gif[/img] 6[img]/images/graemlins/club.gif[/img] 8[img]/images/graemlins/heart.gif[/img] (2 Players)
SB checks, <font color="red">Hero bets $0.20</font>, SB calls $0.20

Turn: ($0.60) 9[img]/images/graemlins/heart.gif[/img] (2 Players)
SB checks, Hero checks

And call small river bet if another heart doesn't fall?
Without the gutshot just bet-fold?


---Out of Position

Preflop: Hero is dealt J[img]/images/graemlins/heart.gif[/img] T[img]/images/graemlins/diamond.gif[/img] (5 Players)
2 folds, BTN calls $0.10, SB calls $0.05, Hero checks

Flop: ($0.30) 3[img]/images/graemlins/heart.gif[/img] 8[img]/images/graemlins/club.gif[/img] T[img]/images/graemlins/heart.gif[/img] (3 Players)
SB checks, <font color="red">Hero bets $0.30</font>, BTN calls $0.30, SB folds

Turn: ($0.90) A[img]/images/graemlins/heart.gif[/img] (2 Players)
Hero checks,

Should this be a bet? I was thinking check-call because I have a decent heart.
How about if I don't have a heart, check or bet-fold?