U R ver e good at abbrev's. Linux uses standard "C" libraries, usuall GNU Lib C (GLIBC). I can't help you with real-time programming in Linux or the kernel. But there are very good how-to's on (e.g.
www.tldp.org). The "The Linux Kernel Module Programming Guide" might be interesting. I remember there was a Kernel Hackers Guide as well.
I also just found a link to a free online book, Linux Programming, on:
http://www.advancedlinuxprogramming.com/downloads.html
Check it out ...
The Linux Kernel is very special, as you will find out, as it hooks into everything ... it is the CORE of everything. There is a special filesystem called the PROC (The /proc File System) which provides hooks into a lot of things. Systems Administrators often tweak System settings through the PROC filesystem.
Red Hat Linux also provides some manuals/guides on:
http://www.redhat.com/docs/manuals/linux/
Good Luck on your Project!