Engine and battery problems with my 1989 Buick Reatta

First problem: Since a couple of months when I drive my buick it turns well for about 5 miles and then it started to run choppy and loosing power once in a while and now it's every time I drive it. What's the problem?

Second problem: A year ago I had a problem with the battery alternator which overcharged the battery so I get it changed. SInce this time I have replaced the battery two times and today it broke up again. It seems there is a shortcut inside the battery because it doesn't want be charged again. What can I do?

Thanks a lot to the people who can help me. I'm 23 and I really like my Reatta.