I'm not sure what you mean when you state that your boyfriend is an "illegal." He has never been in the United States? Then he is surely not an "illegal" for US immigration purposes. After you marry in Mexico, you may begin the process to help him to apply for permanent resident (green card) status in the USA. I suggest you consult with an immigration attorney to have the best chance of success with the whole process.
You may file your naturalization application 3 months prior to your 5-year anniversary of being a permanent resident. I have no idea about the USCIS website, but as you will see from my answer as well as that of my colleagues, you may file 3 months before your 5-year anniversary.
Marriage fraud and visa fraud are two separate things, but both are serious. I suggest that you consult privately with an immigration lawyer about the situation, rather than posting on this public forum.
It would be best for you to consult with an immigration attorney. When you file on the basis of marriage to a US Citizen, the N-400 application specifically states that you must submit the tax returns. If you filed as "married filing separately," USCIS might ask you why you filed that way, rather than jointly. If you filed as "single" or as "head of household," that could cause more serious problems. Best to consult with an attorney.
There is no new law. It appears that you are referring to the fact that the F2A visa category, at this time, is "current" through September 2013. Although we are not sure, it appears that beginning in October 2013, the F2A category will go back to a waiting period before a beneficiary is eligible to apply for permanent resident status. I advise you to consult with an immigration attorney about the particular facts of your situation, to plan for the best options available.
It's not clear at this time whether he is being detained by state officials for the DWI, or by immigration officials for his immigration-related situation. At any rate, it appears that your dad needs legal assistance with BOTH the DWI situation, AND with his immigration situation. As my colleague mentioned, your dad might be eligible to request a bond to be released from immigration detention. You should consult with an immigration attorney for help with the situation.
Did you receive your employment authorization card? If you want to change the name on that card, you would need to file a request with USCIS. To change your name on your Social Security Card, go to a Social Security office with your marriage certificate and ask for a name change. Social Security might tell you that you need to change your name on your employment authorization card.