1. Being in F-1 status does not prohibit you from marrying someone in the US. (But see the answer to Number 3).
2. The naturalization process varies by district. Sometimes it can take up to one year or longer. He should consult with an attorney to determine processing times.
3. Even though you are not going to be filing an I-130, you still may have problems entering the US if you are married to a permanent resident. Every time you enter the US, it is in the discretion of Border Patrol to determine why you are coming in to the US. If you are married to a permanent resident, they may make the assumption that you are not going to abide by the terms of your F-1 visa (i.e., leave the US), and that you have intent to remain here.
You should speak with an attorney and discuss the pros and cons of marrying now and filing any other applications with USCIS.
Note: The content of this reply does not constitute legal advice or create an Attorney/Client relationship in the absence of an agreement for legal services/retainer with my office. This is just a place to start in deciding what to ask your lawyer.