NL5-Unsuccessful resteal situation

Poker Stars, $0.02/$0.05 No Limit Hold'em Cash, 8 Players

Hero (SB): $5.14 (102.8 bb)
BB: $5.97 (119.4 bb)
UTG+2: $3.46 (69.2 bb)
MP1: $4.29 (85.8 bb)
MP2: $3.81 (76.2 bb)
MP3: $6.65 (133 bb)
CO: $5.70 (114 bb)
BTN: $5.80 (116 bb)

Preflop: Hero is SB with A 6
5 folds, BTN raises to $0.15, Hero raises to $0.45, BB folds, BTN raises to $1.10, Hero calls $0.65

Flop: ($2.25) 3 J 9 (2 players)
Hero checks, BTN bets $1.35, Hero raises to $4.04, BTN calls $2.69

Turn: ($10.33) J (2 players)
River: ($10.33) 2 (2 players)

Results: $10.33 pot ($0.43 rake)
Final Board: 3 J 9 J 2
Hero showed A 6
BTN showed ......

Sorry for my english. I recently started to learn it.

Villain is 14/10 over 268 hands.
Atempt to steal - 46
3bet - 5
Fold to 3bet - 80
Fold to resteal - 67

So it is not a good sample to rely on his folding tendencies but definetely we can assume that he plays a lot of cards on the button and he can find fold buton to 3bet.
My preflop plan was to make him fold. When he 4bets my pot odds are 3,5 to 1 (if I did the math correctly) I call because I think I get a good price and when i hit my flush he will pay me off because he is showing a very strong range by 4 betting me. I am not sure about that play though because of low SPR after call. What do you think guys?
After his 4 bet I put him on something like this:
Preflop range: {JJ+, AK}
I think he cbets all his hands OTF. I assume that he would fold AK combos after my shove (maybe except AdKs, AhKs, AcKs) - it would be 6 combos folded out of his 30. It gives me 20% fold equity and after he call my shove with {JJ+}, I still have 40% pot equity and I get breakeven pot odds - slightly better than 40%.

Questions:
1) Is this right that even I get breakeven pot odds in shove situation it is profitable play because of 20% FE? Or maybe I should just call the flop and x/f turn if I don't hit my flush.

2) What do you think guys about my thought process on preflop game? Was it correct to 3 bet? Was it correct to call Villains 4bet?

3) What do you think about assigned preflop range to Villain? Is it reasonable?

Thank you guys in advance for your insight.
I didn't show how the hand ended because I think that lack of this information will serve better to our discussion. Of course I will show it later.