The door hinge is one problem. You can either replace it with one from a used car or buy a new one. Or you can swap your back door hinge up to the front since it's used less.
That may fix the alignment and keep the door closed. Or the inside of your door is getting oxidized on the moving parts. Is your handle hard to pull out and return? If so, some well placed lube may free it up, otherwise you may have to replace the handle.
Getting the doors back on and lined up can be a pain (especially alone), but tightening the hinge bolts so that they just barely move will allow you to line it up, then carefully open the door and tighten them down. I use pin stripe tape to mark a line down the doors, then remove it when done.

I know on mine I've replaced all of the handles at least once, drivers three times, and two of them twice. The crap gets in there and makes the handles really rusty.