How can I check that GCC is installed correctly?

Just type on the commandline:

gcc -v

(give you both version and programs invoked by this compiler)

gcc --version 

(give you the gcc version)

Or you can also create a Hello World to see if it links and compiles properly. Create a file named test.c with the following in it:

#include <stdio.h>

int main() {
    printf("Hello, world!\n");
    return 0;
}

Then, open a terminal and change directory to where you created the file, and run this:

gcc test.c -o test
./test

If it prints Hello, world! on the terminal, it's properly installed and ready to compile.

which gcc

will enable you to know whether gcc is installed in your /usr/bin folder or not