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Is it possible that a past Progress Group Leader's PID gets reused by an other process and this latter process starts a new Process Group? In this case the first created process group and the second one have the same PGID, which situation should be avoided I consider. Does Linux avoid assigning a PID which is a valid PGID?

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No, that's not possible. It's forbidden by the standard:

The fork() function shall create a new process. The new process (child process) shall be an exact copy of the calling process (parent process) except as detailed below:

  • The child process shall have a unique process ID.
  • The child process ID also shall not match any active process group ID.

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