If you do not already have an attorney, I recommend you speak to an experienced immigration attorney in Chicago. You will need to get married and then submit the adjustment documents through the Court. You will then need to be scheduled for the interview.
It can be a drawn-out, confusing and document heavy process from beginning to end that involves different federal agencies, especially since you will still have the Asylum case. Also regarding the pensing marriage, there will be a fairly high burden against you that will need to be beat to show its legitimacy, as you will have gotten married while under removal proceedings.
You need to contact an immigration attorney in your area who can help you with filing the I-130 and dealing with the pending asylum case. Merely getting married is not sufficient. You will have to prove that the marriage is bona fide and not merely done to avoid deportation/removal.
It is impossible for anyone to tell you how long it will take to get the I-130 approved. Your biggest concern now should be retaining an attorney who can help you with your case.
If you are in removal proceedings, the Immigration suspects that you marry somebody to avoid deportation, hence, you need to overcome their presumption that you are marrying somebody in bad faith. I strongly recommend to have an attorney guide you through the process. Do you still have an F-1 status?
I agree with my colleagues that you should consult with local counsel that is experienced in immigration, specifically removal proceedings. Your situation can be complex and confusing. Since you are in removal proceedings, once you are married, you may get your wife's I-130 petition expedited with the assistance of the government. There are other issues to discuss, but more information would be needed. Feel free to contact me or another immigration attorney who is experienced in removal proceedings. Best of luck.
You must have overwhelming evidence of the good faith nature of your marriage. Also, you must have evidence to confirm that the asylum application was not frivolously filed. You can check the I-130 processing tme at www,uscis.gov. Once approved, you can seek adjustment in Immigration Court. Please seek the assistance of a local lawyer.