Answer 1

If it's just some C code you downloaded then the exe is enough.
But there are also externally linked libraries. If you have a look around in your "C:/Program Files" you will see a lot of .dll files, that sort of thing.
Really depends on what you are doing.

Answer 2

It should, since the compiler and linker combine it all to an exe, right?

Excited to hear more about details and pitfalls .

Answer 3

THE TRUMP AFAIK gcc is the gnu C compiler and does not contain libraries. The source code for stdio.h should be available with a standard Linux, MacOS (and I am guessing Windows) distribution/version and after compilation will be statically linked to form your executable.

Answer 4

What Sonic said. Chances are your exe is self-contained and you can send it off to another windows PC. The target PC does not need gcc installed.

You can compile all your headers/libraries to .o files first and link them later to form a .exe if you choose to, or just do it all in one go straight from the source. Anyway the .exe has everything it needs.