You probably aren't going to like this answer, but here it goes. The fact that it is a SkyWest flight is not the issue. The issue here is solely on United. At this point in time, United has no way of listing ahead of time for the jumpseat. You'll just need to show up at the ticket counter and request to fill out the paper jumpseat form for the particular flight. At that point the ticket counter will "list" you for the flight. As for a checked bag, I dont know what to tell you. My hope is that the ticket counter would be used to this sort of thing and know exactly how to handle it.
As for your other question. If you have a mobile device capable of running the United app, you can look up any flight, its stand-by list, and available seats to see exactly where you stand within the app and without having to have an account. Hope this information will help you.