1. Yes. Almost the entire Linux kernel is written in C (with some ASM). Thats not going away any time soon. There are literally thousands of other open-source projects out there using C. Great resource to learn from.
2. Maybe someone else can answer this, I have always just used 'vi' as my development environment.
3. Unlike Windows, Linux is designed in such a way that even if your app crashes, it wont take the whole system down with it. It is possible to write a program which will consume all the memory/disk available, but that is slightly different... There may be an easy solution to that, but I am not aware of it.
4. Other than the socket (networking) interface, most things are identical for a CLI program. If you are designing a GUI, then obviously the two platforms diverge greatly.
HTH