If you have a digital voltmeter you can check a few important things.

With the engine running (since that is when you have the problem) and the
headlights on measure the DC voltage between the engine block - anyplace on
the engine, actually - and the chassis. There should be negligible voltage
between the two. If there is voltage the engine ground is not connected and
that will certainly cause all sorts of weird symptoms.

Also with the engine running, check the DC and AC voltages across the
battery. The DC should be 14 volts +/- about 1/2 volt... higher when the
alternator is cold, lower when it is hot. The AC voltage across the battery
must be less than 0.1 volt. If it is higher - often over a volt AC - either
the battery is seriously bad or the alternator has bad diodes. Replacing the
battery or even connecting another one across the existing one with jumper
cables will tell the difference.

If that doesn't show anything obvious, you are probably going to have to
verify grounds behind the dash and probably under the hood. That is much
more easily done with a Helm manual (about $60 US IIRC from Helm
http://www.helminc.com ) because of their comprehensive wiring information.
The grounds can be checked by measuring (engine running) from one ground
point to any other. If they are the same voltage you need to keep looking.
Maybe the wiring diagram will even point to a ground that is common among
the circuits that are acting up.

Mike