Back Hatch keeps opening up

check with the dealer or on a government site to see if there was a recall

Wouldn't it have been nice if you had reviewed this before you bought this POS? Now you're going to have to deal with Buick dealers as the car's still under warranty, and I hope you got that transferred to your name.

Try taking the battery out of the key fobs, if it'll run without the fobs. If the problem goes away, one of the fobs is bad. Replace both of them. GM isn't going to do anything about this because electrical problems that usually can't be fixed are normal for a GM. Has been for at least 20 years now. Along with premature engine and transmission failures. Good luck to you! Jim