If you just want to execute the shell command in your c program, you could use,
#include <stdlib.h>
int system(const char *command);
In your case,
system("pwd");
The issue is that there isn't an executable file called "pwd" and I'm unable to execute "echo $PWD", since echo is also a built-in command with no executable to be found.
What do you mean by this? You should be able to find the mentioned packages in /bin/
sudo find / -executable -name pwd
sudo find / -executable -name echo