Is it possible under federal law for a convicted felon, not on probation or parole, to get his or her passport?

Yes, you can get a passport but you need to look into the country you plan on visiting as far as their restrictions are concerned before you visit that country.

Yes, a felon on parole can get a passport, it is merely a national form of ID. Now if you want to leave the county, you also have to get a visa from the nation you want to go to, so getting a visa will be harder.