Admitted name fraud when we applied for I-130 year 2001. I-130 was approved. I-485 was denied. What's the best thing to do?

From your answer there is no appeal available to you. There exists no administrative appeal to the denial of an I-485. You do have a right to file a motion to reopen based upon new evidence but that expires 30 days after a decision denying the case. You do have a right to reapply at any time and to do so again if you are placed in removal proceeding. If you get divorced, you will become ineligible for adjustment of status anyway so there would be no point in doing so. If you do refile in your situation you definitely need to consult a lawyer because of the risk of a second denial and that of being placed in removal proceedings.

However, just because you are separated does not render you ineligible for adjustment of status. Since the I-130 has been approved, the marriage has already been deemed bona fide at its inception. However, you would still need to have your husband sign the affidavit of support before it could be approved. Again I say, do not file an application in this circumstance without a good lawyer.

Also, you would of course need a waiver for the fraud which requires that you show extreme hardship to your ctitizen or permanent resident spouse, or parent. Unless your parents live here and depend on you it would be extremely difficult to do this since there would be little hardship to your husband if you were deported since you are not living together.