If you are applying for a change of status at a USCIS Service Center the processing time will vary according to case load. check processing time.
If you are applying for a visa at a U.S. Consulate, and your visa is approved your passport will be returned to you by courier within a few days of the interview
F-1 and F-2 are admitted for 'duration of stay'. As long as the principal F-1 maintains status as a student the F-2 is not required to seek extension of stay.
Yes, you may apply for change of status while on F-2 visa.
However you can not take up the new activity/endeavor until the change of status is approved.
No, there are no travel restrictions on F-2 visa. You may travel as many times as possible, provided you maintain valid F status.