It sounds like two separate issues with your car,

First the battery and alternator and charging:
With the engine running you should get about 14.0 VDC at the
battery terminals. With the car shut off you should see 12.6VDC
at the battery. If you see less, say 8 or 10 V, then you likely have a dead
cell or two, which you can confirm with a hydrometer.

Your battery cables and terminal ends are 16 years old and need careful
checking especially where the cable end fits into the crimp terminal.
Corrosion and vibration can wreck those terminals over time.
Same deal with the starter and alternator cables and pay close attention
to the D+ wire with it's innocent looking spade lug. If it get ratty then
the alternator wont charge. Double check the connections at the battery
clean and regrease. Then service all your grounds, they are critical too.

As far as the revs, that sounds like you have a vacuum leak, which is easy to
get with working around crusty old vacuum hoses. It might be a good idea to
replace all the Vac hoses and elbows and save yourself the aggravation of waiting for them to crap out at the worst possible moment.

Good luck,

Bill