It's the impact that causes a lot of problems. If you can reduce amount of impact and give your body enough rest when it needs it you'll be okay.

For your skipping I wouldn't do it while wearing boxing shoes, they're made to give you traction on a canvas, not to cushion your step. Get a good pair of running shoes that are made to take some of the shock. Do your skipping on something that has some give to it, floor boards is better than asphault, there's one thing that I found that does the trick no matter where you are. Go to a sporting goods shop and pick up some foam yoga matts especially the kind that go together like jig saw pieces. I've even seen something similar at autopart/hardware stores.

The last thing is when you're skipping is to not jump so high for each jump, instead jump just enough to clear the rope. You can still do the double jump and the other techniques provided that you've taken out a lot of the impact from the exercise.

The same goes for your roadwork. Avoid running on hard surfaces, get a good pair of running shoes, and invest some time learning pose and proper running technqiue.