92 Lincoln again

What I was saying was I have a 92 towncar exec 4.6 im getting the tensioner fixed but I heard it could be the altenator it was screaming for a few days then it popped (s belt) it overheated when it popped and I putting a neew belt on while hot tryin to start it the belt popped that was 2 months ago the car still starts now but the battery light is on and wont go off the car sounds fine just missing a belt im gonna make repairs I just need to know what and did I do any damage to the engine and why does my door not close?U have to flick the switch up on the door how can I fix it and the back door doesnt lock it stays upright