Ok, was doing a little bit of research and re-reading of my policy.
What "the fixer" posted seems accurate from what I can tell. Your health insurance (or lack thereof in your case) covers your medical expenses. Liability coverage covers property damage (fixing their vehicle/house/fence) and bodily injury covers their expenses, up to to whatever limit you have paid for. This limit is per person and per accident. So if you have 100K/300K coverage, it covers 100K per person in medical expenses, up to 300K in total expenses for that one accident. So basically it covers for up to 3 people (though it could cover 4 people or more, as long as their total expenses didn't exceed $300K).
Uninsured/underinsured motorist seems to be covering your own bodily injury claims, if the other person doesn't have insurance or doesn't have enough. If they do have insurance then your claims are reimbursed from that. Not sure how "no fault" might affect this.
If you are injured, and have no health insurance, you will be paying out of pocket (at least until you get your claim check, if you get your claim check). You will make claims against their insurance (if they are at fault) or your own (if they are uninsured and at fault). If you are at fault and are injured, I think the only thing that covers you is your health insurance, or if you personal injury protection (PIP) fixer mentioned. I've never had to make this claim, and it may vary depending on your contract. I'd contact your insurance provider with any scenarios you may be worried about and ask them what would be the worst case scenario for your expenses.
As far as the umbrella policy question I opened up before, and insurance overlap... the intent of umbrella policies is to pick up where your other insurance leaves off. So in the example above for bodily injury for $100K per person and $300K per accident, if the medical expenses of a person you injured were > $100K you could be sued for the remaining portion. Umbrella policies might be for $1 million, or $10 million, depending on how much you want to pay (and how much insurance you want). But they generally minimums where they will kick in. So they might only kick in after $100K of payments for bodily injury you caused to someone else. This means that if you injure someone and they have $800K in medical expenses, and you have the liability coverage of $100K/$300K and an umbrella policy up to $1 million, you won't be paying anything (besides your premiums). If you have lesser liability coverage (say $50K per person) and the umbrella policy, then your car insurance would cover the first $50K, you would have to pay another $50K out of pocket, and then the umbrella policy would kick in at $100K. Though depending on your policy they might just require you to up your auto policy before they will agree to cover you.
How much is enough? Don't know. Depends partially on your assets. However even if you don't have a lot of assets yet, don't forget that you can be sued for future earnings. So you may end up working the rest of your life paying for someone else's injuries. Umbrella insurance can be relatively cheap compared to the amount covered, mostly because it doesn't kick in until you reach a very high claim amount. I think looking into the umbrella insurance is sort of like the high deductible plans MMM recommends. You pay for all the smaller expenses you think you can handle, but it covers you for catastrophic situations that you wouldn't be able to recover from. How much you need depends on how much you could lose (i.e. how big your assets + earning potential is) and how likely it is that you are to need to make a claim (if you own a lot of rental property, much more likely someone will take a spill on your property and sue you). If you rent and ride a bike most of the time, and don't have much in your stash yet, you don't need much.
