Prior to 1999, the USIA handled all J-1 waivers. The agency was abolished and all J-1 Waivers are now under the jurisdiction of the U.S. State Department, Waiver Review Division.
It depends. The National Interest Waiver and J-1 Waiver application process are determined independently of one another. One petition does not affect the other.
Yes, you are eligible to self-petition for either Persecution or a Hardship Waiver. However, a No Objection Letter Waiver request must be made by your home country or country of last permanent residence. Additionally, an IGA Waiver request must be made on your behalf by an interested government agency.