200NL ATs on rag flop against moderate 3-bettor

[Dulce Liquido]

Villain 3 bets approx 15% of hands out of the BB, C-bets most flops.

Seat 1: Hero ($261.40)
Seat 2: Villain($200.00)
Hero posts the small blind of $1.00
Villain posts the big blind of $2.00
The button is in seat #1
*** HOLE CARDS ***
Dealt to Hero[A[img]/images/graemlins/spade.gif[/img] T[img]/images/graemlins/spade.gif[/img]]
Hero raises to $7.00
Villain raises to $21.00
Hero calls $14.00
*** FLOP *** [6[img]/images/graemlins/spade.gif[/img] 2[img]/images/graemlins/heart.gif[/img] 2[img]/images/graemlins/diamond.gif[/img]]
Villain bets $42.00
Hero raises to $240.40 and is all-in

I don't expect Villain to fold 22+ he may fold AJ - AK, but it's a stretch.

A few Questions.

That said, is this play +EV against an opponent likely to be 3-betting 15% of hands PF from the BB?

It is optimal to just call against an opponent whose is going to shove the turn with that entire range is it not?

Whereas against a villain who is likely to shut down on the turn with his probable 6 outer is it preferential to shove the flop as no further money is going in unless Villain catches?

If this were the first hand of HU, what is your standard line/play against an unknown? Fold PF?, Call PF/fold Flop? Call PF/Call Flop/Fold later streets?, Call PF/Shove flop?

All/any comments much appreciated.