You facts raise serious concerns - The first problem I see with your facts is that you are apparently not afraid to return to your home country. Your comment or inquiry "if I went back" is inconsistent with your filing an asylum claim. The next problem is that your "Tourist Visa" expired as a matter of law when you overstayed your authorized stay as indicated on the I-94 Entry and Departure card. I would advise you to consult with an experienced immigration attorney before you get much further down the asylum road. If there is not strong evidence to support the I-589 you may be able to withdraw the application.
As for the EB2 and adjustment of status - and I doubt you qualify because you are not in good status at time of filing. If you are qualified - that process is completed in the U.S.
Again - If you have compelling facts to support the already filed I-589 - you may want to complete that process but you will need the sage advice of an experienced immigration attorney to have much chance of approval. The EB2 is an entirely different matter dependent on your status and whether you have credentials for advanced degree or NIW etc. Find an immigration attorney.
Win Eaton is a State Bar Certified Specialist in Immigration & Nationality Law
Eaton & Associates
707 18th Street
Bakersfield, CA 93301
Did you timely file for I-589 asylum while your B-2 I-94 was still valid? If as you state you were in "unlawful status" (not necessarily) than it depends on how long you were out of status. If you were lets assume out of status for up to less then 180 days, i.e 179 and then depart for your EB-2 consular processing visa you are OK. BUT if it hit the 180 days and you depart you may not return for 3 years. If more than its 10 years unless you get a waiver BUT there are no immigrant waivers for EB-2 applicants. There is a INA 245(k) waiver for employment based visas for a maximum of 6 months of being out of status but not more. There is an INA 212(d)(3) NON-Immigrant visa waiver BUT you would be applying for an immigrant visa. I would highly recommend you consult with competent immigration counsel BEFORE you decide anything. Once your outside the US your options are severely curtailed.
I agree with the other attorney. Considering you filed for asylum and are now discussing going back home, essentially means you committed fraud. That is a huge concern, among many others in your fact pattern. It sounds like you have tried navigating complex immigration laws on your own and have been unsuccessful. If I were you I would hire an immigration attorney immediately before you further complicate your situation.
Legal disclaimer: The statement above is general in nature, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship.