Answers

The fact that you can lift the door to get it to latch tells me that it is likely the installer did not install long screws through the top hinge into the 2" x 4" or 2" x 6" that creates your opening in your wall. Often installer rely on nails to support the weight of the door, but nails will allow the door to sag over a period of time. Verify that there is at least one, but preferabbly two long (2" at least) screws through the top hinge. If not, you can use a cordless drill driver to run the screws in. This usually easily draws the door back up to where it belongs. This is rarely caused by a foundation issue, or cause for a new door.

You can put a small tack on the top of the door and hang a piece of fishing line down from that to attach the wreath to. Make sure the tack does not stick up high enough to hit the top jamb of the door. We use this method to hang wreaths on the front doors of our model homes. It does not leave any kind of mark when we remove the wreath.