Other immigration document: If you changed your status in the US such as from H1 to a LPR. (If you still have it)
Yes you can apply for PP at the Oath Ceremony. I applied for mine on Feb 24th and got my passport on March 25th. I did the regular processing, not the expedited one.
You could only apply for a passport if you were given a passport application at the interview. That application has "Applied at Oath" written on it or something like that. If you download any application from the internet then you cannot apply at the oath, you must go through the post office.
If you picked up an application at the interview, then YES YOU CAN APPLY at the oath.