Can a female felon join the US military?
No more easily than a male felon. There are some classes of felony convictions that may be waived. For specifics on these it would best to contact your local branch recruiter.
US citizens may join the French Foreign Legion. Iran has peculiar citizenship laws which may not recognize a child born of Iranian parents (whether still Iranian citizens or naturalised US citizens) as a US citizen, and will require that child to perform compulsory military service when he reaches military age. However, most military forces of the world are not as prone to accepting foreign volunteers as the US military is.
It is possible to join all branches of the US Military with some felony convictions on your record. If the convictions are drug related or if you are a registered sex offender, you will not be permitted to join. If your record was expunged, this is no guarantee either; the DOD has access to your full arrest and conviction record.
As long as you are a naturalized US citizen, you can join the military for special operations, whether it's as a SEAL, Special Forces, Rangers, etc. If you are a permanent resident, you can still join the military, but you won't be allowed to join a special operations unit until you become a citizen.
Unless you're a dual citizen you don't have a choice - you need to be a citizen of the country to serve in its military. The above is actually only true in regards to the Canadian Forces - they require you to be a Canadian citizen. You can join the US military as a foreign citizen, provided you've established permanent residence in the US, and have declared an intent to become a US citizen.