I would bet flop, maybe a tad bigger, and for the turn ,depending on what I though about villain (if he is a calling station, if he is aggro), I decide to either value bet or x and give him a chance to spew.
On some run outs we might have to fold on river if V double barrels but overall in 5NLz I expect aggro villains to bet the turn with all of their range and OTR VBet their value hands and give up with their bluffs.
Passive calling stations in 5NLz like showdown, so betting turn against them and x OTR expecting them to x back, if we face a bet I would probably fold OTR as well.
Not sure if my thought process is good so if you disagree or think otherwise please let me know!

I would fold PF QTs on the SB, IMHO.
As played, I would cbet flop about 0,65~0,70.
This flop don't hits your range of 3bet and maybe villian could float.
OTT:
- Over cards: X/C
- Open draw: I could bet 50% or X/R.
What do you think?

Agree with fold pre unless villain is big nit with high fold to 3b.
Flop cbet is good - we need to cbet our tp hands to balance when we want to bluff this flop and sizing is good on this dry board.
Dont want to check flop and let kj aj ak, realise equity.

I like your 3b pre.
You don't have to 3b all the 4QTs combos. It's a BU open, people on these stakes folds a lot vs 3bets, it's a good opportunity to increase your winrate.
CB flop to deny his equity aswell, evaluete the turn but I'm more inclined to CB again most of turns.