header files in C

Should you have to include a header file into its own library? I can't understand why I sometimes, but not always, get compile errors because it's not getting the header file prototypes before it compiles the libraries.

It isn't necessary either, warnings are not errors and differs from errors in that they're not fatal to the compilation process. You should however, like the warnings tell you, include the header file.
Why is it that you don't want to? Minimize time typing? Trust me you're just shooting yourself in the foot, and nuts.