Possibly battery/ignition/wires

You are describing typical loose/corroded/dirty battery connections and cables. Any mechanic should be able to diagnose the location of the bad connection, but the job will go faster if you find a mechanic with plenty of experience working with electrical problems. They will know exactly where to start looking and the most effective tests to perform. In particular, "voltage drop" tests are the most informative, but for starter circuits these are easiest to do with a helper. The tests involve measuring the voltage across two points mechanically connected together while current is trying to flow through it. Ideally those voltages should be 0.0 volts. The higher the voltage you find at a connection, the worse that connection is, meaning the more it needs cleaning or tightening. For starter circuits, the most you're allowed is 0.2 volts across any one connection and 0.4 volts in the entire circuit.

That is a sign the battery is being over-charged. Your voltage regulator is built into the generator and is extremely difficult to replace separately. Standard practice is to replace the entire generator assembly, but be aware there has been a lot of problems for GM owners. Without going into all the theory, it is critical that when you replace an 1987 or newer GM generator, you must replace the battery at the same time unless it is less than about two years old. That is even when it is not causing smoking or other symptoms. Failure to replace the battery is the cause of many people going through four to six replacement generators in the life of the vehicle. The high incidence of repeat failures is reduced by replacing the battery too.

It is also possible for a battery to develop a shorted cell on its own, and that can cause all of the symptoms you have been describing. In this case the place to start is with the new battery, then have the charging system tested. Insist on a printout of the test results or have them written on the invoice, and post them in your next reply. Specifically, I want to see "charging voltage", "full-load output current", and "ripple voltage". Some testers list ripple voltage as a number, but most just show it as "low" or "high". That is sufficient for our needs.