Romanian medical schools are the worst, imo. However, if you must Cluj and Targu Mures are the best, in terms of the quality of education. Targu-mures is a very small city, but the teaching is very good & Cluj is a large well built modern city.
Also, I would recommend visiting the actual universities & doing your own independent research before applying. You can speak with the admission staff once there.
Yes, it is possible.