Go here to see which countries accept the euro and which don't:
http://en.wikipedia.org/wiki/Euro#Usage
They are safe as long as you take a bit of care of yourself. Don't walk alone at night on dark streets. Don't flash jewelry and cash. Don't brag about the amount of money you have. Don't provoke people or animals that might get dangerous. Generally speaking, if you go by the rules of common sense, you'll be fine.
Watch out for the stray dogs (when you see one, I haven't seen any in Hungary, for example), they carry all sorts of diseases and you most likely wouldn't want to be bitten by one of them.
While you shouldn't expect the same amount of English speakers as in Scandinavia or Germany, you'll have no problem finding enough of them on the street to get help if you're in need of it. A little piece of advice: look for the ones that look like high school or university students. At least in Romania, people over 40 usually studied Russian and/or French in school.
I'm not sure about the visas, but you might find this link useful:
http://projectvisa.com/regiondisplay.asp…
I'm Romanian. Depending on how much time you plan to spend here and, of course, your interests, I could come up with some recommendations. E-mail me. Or add to your question and I'll edit my answer.