Hello Sigma Freud,
Seeing as no one else is responding here's my $0.02
I applied and was accepted to CCS but did not end up going. Regarding the application, yes there is a separate one. Most of the information you need to know can be easily found by a quick google. I think they redid their website a couple of years ago around the time I was applying and the process should be clearer now.
I do not think they released any statistics on applicant numbers or acceptance rate but as a rough guide it's about "as hard" to get in as say UC Berkeley.
Also note that the CCS application is subject-specific and it is more competitive for subjects UCSB is strong in (or so I have heard).