USCIS does not have a maximum processing time. The processing time varies by application because each one is unique. You best bet is to hire a lawyer that will make sure your application is in order to reduce delay. You can check on uscis.gov for processing time.
Unless your L-2 status is set to expire soon, you should not have any problem because L-2s are permitted to study in the U.S. If your L-2 status expires before you can file an application to change status to F-1, you would have to depart the U.S. and apply for an F-1 visa stamp at a U.S. consulate.