Q6s BB vs BTN float and bluff catch

PokerStars - $0.50 NL (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

CO: 390 BB (VPIP: 33.33, PFR: 23.39, 3Bet Preflop: 3.23, Hands: 176)
BTN: 100 BB (VPIP: 26.03, PFR: 19.18, 3Bet Preflop: 10.61, Hands: 148)
SB: 146.76 BB (VPIP: 23.11, PFR: 15.57, 3Bet Preflop: 0.64, Hands: 424)
Hero (BB): 38.36 BB
UTG: 100 BB (VPIP: 19.51, PFR: 18.29, 3Bet Preflop: 20.69, Hands: 84)
MP: 321.6 BB (VPIP: 23.53, PFR: 17.65, 3Bet Preflop: 0.00, Hands: 37)

SB posts SB 0.5 BB, Hero posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has Q♦ 6♦

fold, fold, fold, BTN raises to 2 BB, fold, Hero calls 1 BB

Flop: (4.5 BB, 2 players) 7♠ A♥ A♦
Hero checks, BTN bets 2.86 BB, Hero calls 2.86 BB

Turn: (10.22 BB, 2 players) 6♠
Hero checks, BTN bets 6.5 BB, Hero calls 6.5 BB

River: (23.22 BB, 2 players) 5♣
Hero checks, BTN checks

BTN 26/19 148 hands BTN 2/11 18%!
I was expecting based on VPIP and PFR for him to open BTN close to 50% if not more so I decided to flat Q6s OOP.

Flop is super dry AA7.
I feel opponent will c bet everything but Ax here because he has no way to extract the value with it readless.
So I am expecting low pps, 7x, Kx for bluf, Qx,Jx,10x , basically more combos for bluff then for value.
Value really consists of 7x, mid pps and perhaps low pps if he has idea how to play them on later streets.

I decided to call flop, float with bdfd and over card that may be good if I do hit it.
Turn is 6, and I decide to bluff catch vs his double barell bluffs (Kx,Qx and him turning low pps into a bluff)
River is blank so standard c/call was idea behind it.

Questions:

- Was this correct thinking process in vacuum?
- How would you have played the hand?
- Is c/raise an option here in vacuum? What do you do with mid pps here, would you consider check raising them? Basically what range are you c/raising, what are you folding and what are you just calling down.
- How do things change for 100bb vs 40-50bb stacks?

Really appreciate all your feedback!