Here's the Cell SDK, compilers linkers and tools free from IBM.
Have you read that? This is an SDK for IBM Blade Servers, not the PS3. You will not be able to use this to develop for the PS3. with them you should be able to get code up and running if the PS3 does ship with a usable Linux.
No. You wouldn't even be able to do "Hello World". You assume too much. Cell uses the Linux OS, so it'll certainly have Linux installed on the PS3 somewhere.
There is a Cell port of Linux yes. However the PS3 is not going to ship with an fully fledged operating system, anymore than the XBox dashboard is Windows2000. Sure, it might be running a tailored version of the Linux kernel, but there's more to an OS than just the kernel.