It depends on what your conviction was and how long it has been since you were convicted of a felon. The US government has the right to deny a passport application. It is best for convicted felons to consult with a lawyer before making travel plans abroad.
My understanding is it depends on the nature of the felony. You'll want to check with the consulate before you travel so you don't run into any issues when you arrive.
Possibly. It depends on what the felony conviction was for. The United Kingdom restricts some felons but not others, depending on the nature of the crime. Contact the British embassy.
