The hinge side of your jamb is out of plumb. The casing will have to come off to replumb. As for the door being sloppy when closed you may be able to correct that by bending the metal flap within the strike toward the door.

Well, the easiest thing to try first is to take the pins out of the hinges, lay them on a concrete surface, and give each one a modest rap or two in the center; then reinstall. This will bend the pin slightly and provide more friction so the door won't be as easily blown open. IF you need to make the hinge stiffer, take the pins back out and bend them a little more.

As for the door having a centimeter of play when closed...something is wrong here. Do you have a strike plate installed? If so, there should be minimal play once the bolt engages with the hole in the strike plate. Provide more details.

Thanks so much. I found a temporary, easy fix.

You know those little velvet sticker things that you can put on the bottom of bric-a-brac to prevent them from scratching the furniture, they're about the size of a thumb tack. We stuck two of them onto the vertical door stop. No more banging noise.