1993 Buick Park Avenue Battery change then erratic behavior

13.5 volts is too low. It must be between 13.75 and 14.75 volts. That little difference seems like nit-picking but it can be an indicator the generator has a bad diode. That will reduce its maximum output current to exactly one third of its rated value, and that's not enough to run the entire electrical system under all conditions.

GM has a very high failure rate on their generators since they were redesigned for the '87 model year. They develop huge voltage spikes that can destroy the internal diodes and voltage regulator, and can interfere with computer sensor signals. Anytime you have a failure, replace the battery unless it is less than about two years old. As they age they lose their ability to dampen and absorb those voltage spikes. Since you just did replace the battery, that suggests it was old enough to allow the voltage spikes to be a problem. To see if I'm right, have the charging system professionally load-tested for maximum output current and "ripple" voltage. Ripple voltage is the AC voltage you mentioned but that may not show up with a digital voltmeter at the battery now that it is new. Professional testers look at the rapid variations in output current as well as voltage at the battery.

Sorry to leave you hanging for so long. Had to run out of town.

I'd still do the load-test to verify the new generator doesn't have a problem. As an alternative, you can also look for a high resistance connection between the generator output terminal and battery positive terminal. Turn on a lot of loads like head lights, heater fan, and the air conditioner, then measure the voltage at both places. The readings should be within a couple tenths of a volt.

If the problems occur with the air conditioner running but not with just the heater fan on, that would suggest a slipping drive belt although there should be a lot of squealing with that. The air conditioning system only draws a couple of amps more than the heater fan for the compressor clutch, so if that causes the symptoms, the compressor may be loading down the belt. Look for a spring-loaded tensioner pulley that is rusted tight and not putting enough tension on the belt. If you can see the belt slow down, look at the speed of the crankshaft pulley. It is not unheard of for the outer ring to break loose from the hub. If the pulley is cast as part of that ring, it can slip, although it usually falls off.

By the way, you said you replaced the battery but you didn't say if it was a new one. If you installed a used battery that is more than a couple of years old, the voltage spikes these generators produce are likely interfering with some sensor signals. You can verify that by unplugging the small connector at the back of the generator. If the problems clear up, suspect those voltage spikes.