Immigration officials certainly do a background check on a US citizen sponsoring a foreign spouse. They are mainly interested in whether the marriage is legitimate. If the US citizen has married and sponsored other people before, this may raise red flags.
The citizen spouse has no recourse to the action as US immigration laws no longer allow a citizen spouse to apply for residency for an illegal immigrant spouse. The Mexican national will have to leave the US and file under the required USCIS regulations for reentry.
Yes, but the US citizen should sponsor his/her spouse's immigration in order for him/her to get a green card.
Your spouse has to sponsor you for immigration to Mexico.
They are officially married. One spouse can sponsor the other for immigration to his or her country.
Yes they retain citizenship.
No, she is not. She will be allowed to remain in the US with her spouse and children, but she will have to apply for citizenship separate from her marriage. The US citizen REMAINS a US citizen. The immigrant remains an immigrant and must follow the legal path to resident immigrant status, and from there to citizenship. Marriage is not a free pass to residency or citizenship.
As a US citizen, you can sponsor an alien for U.S. Green Card application for the the immediate relatives of a U.S. citizen, such as your wife. But as a convicted criminal, most likely you are in jail, with little or no income. So it is difficult for you to "sponsor" an alien financially. The USCIS Form I-864 - Affidavit of Support is required for family-sponsored immigration. An affidavit of support is a guarantee to U.S. government that an immigrant will not become a public charge. SO you may need a a co-sponsor for her financial sponsor for Form I-864 if needed.
Since marriage to a US citizen confers US citizenship upon the spouse, it is not clear how your spouse is an illegal immigrant unless you are also an illegal immigrant (not that you actually said that either of you are living in the US, but that seems to be the most likely interpretation). I also don't know why you are abandoning your spouse instead of getting a divorce. Nothing will necessarily happen; it depends upon what action the abandoned spouse may choose to take. If you are sued, then there could be various consequences depending upon the outcome of the suit.
If yGetting a family-based Green Card is a two-step process. The first step is the "Immigrant Petition" which establishes that a qualifying relationship exists between the U.S. Citizen or Lawful Permanent Resident and the Green Card applicant. The second step is the Green Card application. If the sponsor is a U.S. Citizen and the Green Card applicant is a spouse, parent or minor childwho is currently in the U.S., then these two steps can usually be combined into one. Otherwise, applicants must wait for the Immigrant Petition to be approved before they can move on to the Green Card application.
An international who is married to a US citizen can get his/her green card in the following manner. The US citizen should file in Form I -130 to sponsor the spouse. The Spouse should then file in form I-485 to adjust the status to that of a lawful permanent resident.
Yes, an American citizen may sponsor a same-sex Mexican spouse for a visa, permanent residency and, ultimately, citizenship.
Through the US citizen spouse can get green card after two years of marriage and after 3rd anniversary can apply for US citizenship using Form N-400.