Voluntary departure is certainly an option, but you will want to talk with over with the attorney representing him with the asylum case. It is not a decision to be made out of frustration. Even if the two of you plan to leave the US for a few years, it would likely mean he would not be able to return with you when you returned to visit family. If a grant of asylum seems likely, or his parents could meet you and you could terminate the proceedings and he could adjust through marriage, these would all be options that would give you both many more options during the years to come.
If he asks for voluntary departure early he can request up to 120 days. You should meet with an immigration attorney though because there might be other options. Even some options to plan for voluntary departure so that he can leave in december.
To answer some of your questions directly, you would not file a I-485 abroad, there are other forms to file.
This answer does not constitute legal advice, and should not be relied on as each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
Lots of questions but impossible to tell. If you want good legal help you must pay for it. Your b/f can request whatever he wants and the Judge may say yes and may say no, its completely a discretionary situation. Filing papers without proper help is a complete waste of money.