Installing a hitch is pretty easy and straightforward. An SUV will have holes on the frame ready to accept a hitch.
The only tricky part is fishing the bolts through the frame and most hitch kits come with a wire designed to help with that.
After that it's literally tightening bolts.
You shouldn't have to do any wiring. Your rear lights will be visible through the bikes. Unless you put a cover on or something like that.