I do not see a problem in a U.S. citizen applying for his wife. In cases where the primary sponsor does not earn enough, a co-sponsor is required. He or she must complete form I-864 along with financial evidence.
As discussed by my colleagues, renunciation of U.S> citizenship is a serious and in most cases irreversible, therefore you should consult with an immigration lawyer before you try this yourself.
A person wishing to renounce his or her U.S. citizenship must voluntarily and with intent to relinquish U.S. citizenship:
appear in person before a U.S. consular or diplomatic officer,
in a foreign country (normally at a U.S. Embassy or Consulate); and
sign an oath of renunciation...
As a student, you may not work outside campus without USCIS permission. Permission is available after the student has completed two semesters of school and can establish Severe Economic Hardship. However, if the USCIS discovers you working without permission you most certainly can be deported. You should consult with an attorney for some advise on your next step.
You are a United States citizen, and you and your fiance(e) are both free to marry, and have met in person within two years.
Documenting the petition. The fiance/e petition and all supporting documents should be filed by the citizen fiance/e with the appropriate USCIS Regional Service Center having jurisdiction over the petitioner's residence. This is usually done in the United States. The new statutory requirements have forced fiancé/e petitioners to document USCIStances where the couple...
If you tell the truth, you will have an excellent waiver application. It should be approved, In my experience, if you husband did not commit any crime, you could file an I-601 waiver, which should reduce his stay abroad from years to several months following your I-130 approval. Understand that obtaining a 601 waiver requires legal skills in it's preparation. You should contact an immigration attorney before you go forward.
From the facts you presented, it would be highly unlikely that he would be approved for an I751 waiver because the burden is on him to prove that the marriage was bonafide. I don't believe he will prevail. Good luck.
Absences out of the Unites States
Count the exact days you were out before you file. You may save time and money. If you apply under the 3-year rule, then you will have to have physically resided in the U.S. for a period of 18 months, and during this time never remained out of the U.S. for a period of greater than 6 month. . If you apply under the 5-year rule, then you will have to have physically resided in the U.S. for a period of 30 months, and during this time never remained out of...