Are the headlights supposed to be on all the time on this model?

What is your question?

I recently bought a 1997 Chevy cargo van and although it was fine driving it home it has some sort of electrical issue. I first noticed that the fuel gauge was bouncing back and forth and problem was worse with headlights on. While driving I could turn heater off and radio off and turn interior lights all the way down and it would stop. I put a new battery in it but that didn't help. I thought maybe it was the voltage regulator in the alternator but just yesterday i noticed that the passenger side headlight was much brighter than the drivers side and when you turn the brights on the drivers side gets bright and the passenger side goes dim? Any suggestions? Thanks.