It could well be that you have sucked up water and/or other crud from the bottom of the tank. Try some more to get it purged out. Changing the fuel filter would probably be a good idea too, before very long.

Another, less appealing possibility is that the pre-pump in the tank has failed. They don't like having the tank run down all the way---they tend to run hot if you have less than 1/4 tank, and maybe this one was already on the way out.....

I doubt if the timing belt has anything to do with it, but even if it does, it's not a big deal, in fact, compared to trailing arm bushings it's a walk in the park. Probably wouldn't hurt to put a new one on in any case, as preventitive maintenance, unless you know when it was last changed.

85 is within the range of years for crumbling wiring, which could cause problems similar to what you describe. However, I think you would have noticed it when you replaced the IAC valve, if it was bad. Look closely at the ground bolt(s) on the intake manifold, where a cluster of brown wires are attached. Not a bad idea to take the bolts out, clean everything, and reinstall, to insure good metal-to-metal contact. Doing so will give plenty of opportunities for any deteriorated insulation to show itself.