As a big caveat: the way this all works will vary from state to state, and based on how your policy is written. The best way to answer your questions 100% correctly would be to talk to your insurer.
If you get injured in an accident, typically UMBI is primary, so your personal health insurance kicks in after your auto policy is exhausted. This is helpful because you're not paying the out of pocket portion of your healthcare coverage until after the auto policy is exhausted, so for minor injuries you'll probably have no out of pocket. However, some states allow individuals to designate their healthcare insurance as primary by default, which reverses this equation.
UMBI also covers other individuals in your car, other members of your family, and other people you've allowed to use your car - for instance, if you have a passenger who is injured in an accident (and the other motorist isn't insured), their expenses are covered under your policy. So it's not just about comparing the auto policy to your health insurance, since you're really buying coverage for a number of other people as well.
Proving lost income for the self-employed typically involves collecting a pile of documentation to project income (i.e. past years' tax returns) and/or show lost opportunity (i.e. here's a list of appointments or customers that you had to cancel, orders you couldn't fill, etc.). It's probably best to talk to your attorney to understand what would make sense for your situation so you can be sure you're capturing any documentation that you might need when filing a claim.