Generally if you entered legally with a valid visa and you are seeking permanent residency based on marriage to a U.S. citizen certain violations of immigration status such as visa overstay does not impact the ability to file your application for U.S. permanent residency in the U.S. You should cosnult an experienced immigration attorney for advice pertaining to your aprticular situation.
You have a potential fraud issue that needs to be evaluated. Consult with an experienced immigration attorney who can review your case and advise you how best to proceed.
The unauthorized employment is not a problem, but you could have a problem if there was a misrepresentation to gain entry into the U.S. See my article, "A Lie Can Exclude You From the U.S. Forever", on our website at http://www.immilaw.com/Newsletters/2007%20January%20Lies%20and%20Waivers.htm.
This is only a preliminary response to an inquiry, based on incomplete information. Helpful advice and counsel can only be provided after you have discussed your case with Mr. Bach, he is familiar with all of the circumstances of your case, and the advice is provided in writing. Any opinion provided here should not be relied upon for any purpose. No attorney/client relationship is formed until you have formally retained our law firm to represent you. We are not responsible for any action or lack of action you take based on this preliminary response.
You should be fine to file for adjustment of status as long as your last entry was legal. However, it is important to consult with an experienced immigration attorney to be able to evaluate your prior TN complication. I woud recommend a phone call versus an email in the future : ).