Yes; as a Russian speaker you would be completely fine in Bulgaria. You could read anything immediately and Russian and Bulgarian are similar languages, so you can even learn quickly, if you want.
Well, interesting. I do not like the contemporary Russian regime but it is true that︁ I have not been there personally for many years.
Yes. In the very past, speaking Russian was actually︆ a must to live there comfortably. Maybe times have changed somehow, at least in Moscow?︇ (I do not believe that it has changed at the province.)