Is this how a tight passive player plays a set?

I would fold pre. If you want to play this I would definitely iso-raise instead of just calling his limp.
Limpers can have pretty much anything.. They can limp 84s or Q8o but they also can limp super strong hands like AA,QQ,AK etc... Tripple barrels at very low limits are often quite value heavy. And limpers are usually passive. So now a passive villain is using a very strong line. You can consider folding probably at least OTR.

Fold pre. Maybe isolate his limp with A4s but just dump the offsuit trash hands.

As played, folding to turn pot sized bet.

Fold preflop: A4o not strong enough
Fold flop: A4o not strong enough
Fold turn: A4o not strong enough
Fold river: A4o not strong enough

Just echoing everyone else and saying fold that hand preflop. It’s fine to open with a raise from the BTN if it’s folded to you, but it’s trash otherwise. The suited version would be a standard open from MP for most people, because of the flush and FD possibilities.

Then the problem OTF is that you make top pair with a weak kicker when you do hit, so you can easily be dominated and just donating money to a better ace.

About limping: there’s an old saying that you shouldn’t go broke in an unraised pot. People can have all sorts of very unlikely hands, especially the blinds, because they get to see a cheap/free flop with any two cards.

Ok, thank you all! Will fold it in the future.