I've never actually started a cast from scratch, but I did take over and currently manage the Delaware cast, so hopefully I can be of some help.
You should have no issue with using RHPS assets on facebook or flyers. The worst that can happen is that FOX would say, "Hey, stop that", but it is such a small blip on the radar and in the long run would be making them money anyway. If you are going to use Rocky fan art please be sure to talk to the artist first to get permission. I've been pushing lately to stop the spread of uncredited art shared throughout the community.
Yes, you will need to get the rights to project the movie. If you perform at a movie theatre generally they can handle securing the rights. Instructions for who to contact if you do it on your own are available at www.rockypedia.org/Basics_about_the_RHPS...a_showing_of_RHPS.3F
If you have not yet approached a theatre here is a little bit on information on doing that www.rockypedia.org/RHPS_Casts#How_can_I_...y_cast_to_perform.3F
The Rocky Horror Sourcebook has a lot of good information for once you get your show running. www.rockypedia.org/Sourcebook/Introduction