Stalls / won't start when hot

I have a 94 Corolla with 100k mi. Was my mom's car before she passed
away. She took very good care of it / maintained it well.

Started stalling a few weeks ago when parked at idle. would turn over
but not catch. After 10 min, would start on first try. Started stalling
more often, on the highway, at stop signs, etc, would not re-start for
10-15 minutes.

Replaced wires, plugs, cap, rotor, pcv, ran better but same stalling
problem. Replaced fuel filter, problem went away for a day. Would stall
again, but would start right up. Now if I drive somewhere 10-15min,
does not stall. after parking, go to start it up and won't start for
10-15 min. Then stalls whether at low idle or regular driving. I have
cut into my rotors now keeping it revved up / shifting to neutral to
keep the rpms up so it won't stall, which works for a while but then it
stalls anyway.

Any ideas? I don't have the money for a mechanic to tell me it needs a
new fuel pump, then a new distributor, then the problem is still
there... Thanks in advance.

I replaced it last week. Ran better and didn't stall for about a day. I
thought it may be bad gas but I recently ran it to empty. Is there some
sensors I should check? Seemed to start stalling a few days after I
took it in for an oil change/air filter replacement/lube at Walmart.
What is that electrical sensor sticking out of the assembly connecting
the air filter to the manifold? It looks old.