OP, your questions are pretty basic, and all of us have asked the same questions. That means they've also been answered many times on this forum and others. There's a certain reluctance to invest a lot of time in answering inquiries in the absence of indications someone's first done a bit of research on their own.

In the end, trusting answers you get here (or again, elsewhere) without verifying them independently will get you into trouble anyway. Times change, procedures change, even governments change drastically--c.f., two of your destinations, Abkhazia and Crimea. Plus: we respondents make mistakes...or at least, I do.

The search box on this site gets routinely disrespected, but it actually works fairly well. Insert any obvious search terms and you'll start collecting answers--"green card insurance," "travel insurance for Americans," or "insure motorcycle in Russia."

At any moment not subject to COVID precautions there are probably thousands of US citizens riding motorcycles around Europe and Asia, and sometimes it seems like they're all blogging constantly. Some are quite obsessive about describing where they bought insurance and which border crossings are easiest/fastest/cheapest/most scenic/most fun. Read a few blogs, and take notes.

Last, when asking questions it's usually more productive to be very specific rather than general or scattershot. "Where can I buy insurance in the following 20 countries?" is usually less productive than "Can I buy insurance entering Turkey from Bulgaria?"

Hope that's helpful.

Mark

PS: Travel insurance from DAN covers US citizens cheaply and comprehensively. Read the fine print.