The President's policy announcement should not interfere with somone's eligibility and/or ability to apply for permanent residence. That being said, if you qualify for residence, I would suggest you take that route.
Once the rules are announced, which should be by mid-August, things should be clearer. You and your boyfriend may wish to consult with an experienced immigration attorney for further professional assistance and guidance.
So long as the marriage is legitimate, your brother has the required proof of his lawful inspection and admission, and he has not had any other problems with the USCIS or INS, this should not present a problem by itself. However, it would probably be a good idea for him and his wife to consult with an experienced immigration attorney for proper and professional advice.
You should have received a full transcript of all the hearings before the IJ. No transcript is prepared until and unless an appeal is taken. The last IJ hearing, at which the IJ granted asylum, is probably the first or last of the transcripts, depending on the arrangement of the copies. The most you can do is request an extension of time from the BIA to respond to the government's brief.
Of course, retaining an experienced immigration attorney may be a tremedous help to you as well.
If you wish to change the name on your card now, you will have to file Form I-90 and pay the required fee of $450. It is probably easier (and cheaper) for you to wait until you apply to remove the conditions and indicate that you are taking your husband's name then.
Assuming for the sake of answering that this is for the spouse of a US citizen, it depends on how long it takes for the National Visa Center to do the processing of all the required paperwork and documents, and then how much of a backup the particular consulate may have on their interview calendar. Most medical exams do not take that long, and the results are usually available shortly thereafter. Depending on the individual Consulate's rules, the medical results may be picked up by the...
It may be difficult for you to withdraw your Affidavit of Support. You would need to contact the National Visa Center and have the NVC case number and other information ready to give the person handling your call, and you may not have this information. If you don't, you can try calling anyway and explain that you want to withdraw the I-864 for this person; you shouldn't need to give a reason, other than you changed your mind. The telephone number for the NVC is (603)334-0700.
As I wrote in answering your prior posting, you need to consult with both a criminal law attorney and an immigration attorney as soon as possible. These arrests, if not tended to properly, can be major problems for you if you end up being convicted on the prostitution charges. The criminal attorney, working with the assisatnce of the immigration attorney, may be able to get the charges reduced to something which will not pose a danger to you.
Don't waste time; you need to attend to these...
I-601 waivers can be challenging. I have found psychological evaluations of the qualifying family members to be of value as part of the evidence presented. I would also say that you would be best served by retaining an experienced immigration attorney to help.