What are the requirements to convert a license from Iran to USA?
You cannot convert the CPL to FAA-CPL. What is possible is to obtain a FAA-PPL certificate by verification of the your current foreign license. This certificate will be valid as long as your foreign license is (plus medical conditions, and 24-months PPL flight review required for any PPL in the US).

With the PPL certificate, you will be able to obtain IR and CPL:


Pass IR and CPL written tests.
Attend training for IR and CPL practical checks.
Accumulate at least 250 flight hours. Time in the foreign country with the foreign license will count as well, but at least 3 hours are required with the FAA instructor. The instructor will vouch for the candidate is ready for the check-ride.
Pass CPL and IR practical checks.


A valid residence permit will be necessary to use the FAA-CPL.

The CFI roadmap is similar, written tests and checkrides are mandatory, there no minimum hours to be flown in the US. As a large part of the knowledge required is similar to many ICAO-member countries (teaching, meteorology, navigation, aerodynamics, etc) this shouldn't be a problem to be certified FAA CFI.



Related:


Do I need a PPL license for a CPL license?  
I have a European EASA license - what do I need to do to be allowed to fly in the US?
Can a pilot with an ICAO Multi-Crew Pilot License fly an airliner into the U.S.?




References:


Required knowledge FAR 61.123 et seqq.
Required flight experience FAR 61.129.
Pilot certification in the US on Wikipedia.  
Process for foreign CPL to FAA-PPL conversion (FAR 61.75).
Flight Instructors FAR 62.181