I'd be happy to answer your questions!
Currently, the cloudBit cannot be used without our cloud server.
Also, we don’t officially support direct access to the operating system, but it’s a linux system so you could research and apply most concepts to the cloudBit.
However watch out!
If you make changes here you could affect the ability of the cloudBit to perform normally and this will void the warranty. Although, being makers, we generally encourage tinkering. You can restore/update your cloudBit firmware at any time with this tool (firmware is in the microSD): http://littlebits.cc/cloudbit-firmware