There is possibly a misunderstanding. CtrlC does not generate a signal. It is perfectly possible to press CtrlC anywhere, and no bad things will happen (for example in every text editor or word processor, that's the de-facto-standard for "copy").
However, when you run a program in the shell, then your keypresses really go into the shell, not into your program. The shell will forward (almost) everything to your program's stdin, and forward anything coming from stdout to either the terminal or another process or a file (if you used a pipe or redirection).
If the shell sees you press CtrlC, then the shell sends the interrupt signal. But that's really just something the shell does, not something that magically happens because of the key combination.
About CtrlX, you probably meant CtrlZ. This stops a process, and the shell outputs a number which you can use with fg
to make it run again.