Lets see, you can write code in unix with any of the myriad of text editors available - try to familiarise yourself with either the vi or the emacs editors. For compiling code, you can use the GCC (have to install it seperately - though it will usually be available on Linux by default). Many systems come with their native C compilers, like Sun Studio on Sun or HP's HP C compiler.
On almost all systems, the libraries are available under /usr/lib, while includes are under /usr/include. Both libraries and include files specific to a certain products may be installed elsewhere during product installation as well.
As for debugging, you can use GDB which is part of the GCC. For more info on GCC, go
here.