If I get convicted of a felony can I legally exit and enter the country if I already have a US passport?

As long as you are not wanted under a warrant and are not on probation without written permission to leave the country you should have no problems.

If you are a US citizen and have a passport, you may exit and enter the US. You may be restricted by other countries as to entering their country, So you will need to find out about the other nations visa requirements for entering their country