If I am a convicted felon, is it possible to get my passport and right to leave the country?
Assuming that you are not still on probation, you can obtain a passport and travel freely. The only exception might be if you are traveling to a country that has a prohibtion against entry by felons, for example Canada. What you should dio is to check withe the consulate of the counrty that you are going to travel to; they can let you know what restrictions, if any, you can expect.