I can lone afford liability. If someone hits me and it's their responsibility; will their insurance cover my damages?

Answers: If they own insurance. If they don't your car may not get fix for a long time. You may come to an end up suing etc. and you'll be out a car this entire time. It would be their responsibility though.
Yeah, as long as the other party is 100% at scorn, you can settle with their insurance. But please consider sacrificing something else to go and get collision and comprehensive coverage, particularly if your vehicle is under 10 years older. If something happened to it, and you couldn't get it fixed, it would be far more financially devastating than paying for the coverage up front.
It may, but ask yourself one incredibly important question.

You speak you can only afford liability. Full coverage is only $100 or so more.

Now, let's influence you get into a wreck, your fault, can you afford FAR MORE than $100 within repairs that you will have to pay since you hold such a cheap insurance?

And if you can't, what sense at all does it make, to move about with the cheapest insurance?

None.

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