I had no problems at all buying a car--it's legal. It will be trickier though if you have to finance it as you won't have credit history in the country. There aren't problems with your license, but with proving you can pay for it. I bought my first car outright b/c we got a cheap little car I paid cash for. Our second, nicer car, I had to use my husband's credit history to buy in his name (even though ironically it was my income we were living on at the time.)
I'll leave the insurance questions to others as I started with my USAA insurance and carried it over here to an overseas policy.