98 honda accord lx dash lights come on and battery smokes?

Okay when I bought the car a belt was sqeeking I believe it's the one connected to my alternator the serpentine belt I believe not 100% sure but I made it tight and stopped the squeaking so months later my main headlight bulb blows out nothing wrong drove to work and back fine next day turn my car on to get a new bulb my battery light door lights and another light comes on can't think off top of my head. Car runs fine my radio would go off and on sometimes then got a new bulb and had my battery tested it was fine and switched out my bulb and after that my bright head lights blow out so I drove it to a town a hour a way and back during that time my radio would stay on and threw the whole time my dash lights would go off and on and realized they only come on while I push on the gas so later on the road my dash lights wouldn't come on so figured my car was alright by the time I got home my battery under the positive side was smoking. And had a funny smell I turned off my car took the positive off it was very lose and waited fo mechanic looked at it she found a wire which is my negitive ground wire was pretty much done it was open and blueish green so I bought all new ground wires and clap and tighted my positve clap. And charged my battery and said it was maintaining its charge And still same problems my car still runs but unsure of the problem and don't want to drive it to cause more damage any help you can give me it's very appreciative and am on a very very tight budget.

Have your alternator tested

I will thanks