Is it true that if I was put on probation in MD that I can only live in Maryland and not allowed in DC or VA?

It is a standard term of a probation contract that the probationer not leave Maryland without permission. Some judges will change that condition to permit a person to travel within the DC Metro area. You should review your probation contract to find out what the terns are. If you plan to move, you should discuss the situation with your probation officer to avoid trouble down the road (and a possible violation of probation).