I am in a band; can I use Creative Commons licenses but still collect statutory royalties such as under statutory licenses for public performances?
Yes, so long as you choose a “NonCommercial” license option (ie. Attribution-NonCommercial, Attribution-NonCommercial-ShareAlike or Attribution-NonCommercial-NoDerivatives) because under these licenses you reserve the right to collect royalties under statutory or compulsory licenses for commercial use of your work. Whether, as a practical matter, you can collect these royalties, depends on which country you are in (check out the answer to the next question). Under the Creative Commons licenses that permit other people to make commercial use of your work (ie. Attribution, Attribution-ShareAlike, Attribution-NoDerivatives), the licensor waives the right to collect these royalties.