Mobile home repairs? Can a contractor do them?

Any competent tradesman should be able to do that stuff. Unless your mobile is very old. most of it will be very much the same as the same stuff in any house and if it isn't then someone with a little experience ought to be able to figure it out. Just make sure you get someone licenced and properly qualified for the plumbing and electrical. Ask around for a good contractor, or simply an experienced carpenter who can assess what order you should be doing things in. What he can't do, you get the electrician and plumber in for. If you can't afford it all at once, electrical is where I'd put my money first because it's a safety issue. Plumbing next, then probably the floor if it's structural. If it's just replacing floor coverings, do that last.

You're going to find that everything about a mobile home is different than a stick built house. Standard doors don't fit, the plumbing uses different materials and even the wiring might be aluminum rather than copper. As a journeyman pipefitter with an electrician girlfriend we highly recommend that you switch everything you repair/replace to common materials. Especially, get rid of the plastic hose plumbing and the inferior wiring. Any contractor can do that.

You don't need anyone special. Any handyperson can do the jobs you listed.

Be careful how much you invest. Too much, and you'll probably spend more than the house is worth.