For the Firefox in full screen kiosk mode, there is a addon that will run it in that mode specifically.
Clearing data and history is a setting in firefox itself. Edit, Preferences, Privacy, there is a spot marked Privacy Data that has a check box to clear both on shutdown.
For getting Firefox to start up automatically it needs to be in the session run list, like irlandes, not sure exactly for IceWM, but gnome has a session list of all process that are to be started on bootup, make sure firefox is one of them.
Loading only allowed sites, will use a filter/blocking plugin is easiest, one thats modifiable is best. The addon lists at Mozilla.com has a good selection to choose from.
I found a listing for an old walkthru on how to set up firefox as a kiosk for a university student union in IceWM, it might help with some of the particulars (think they were using Red Hat). http://www.unc.edu/~payst/?p=2