First of all, thank you for the quality of the response, it is very, very complete. The 777 in emission was just the time to try, I immediately returned to 644.
I am a fan of prime mover because often the other solutions have all caused me problems. PM is the only plugin that is as flexible.
I managed after numerous attempts to find a solution thanks to an old backup of my wp-config.php that I simply replaced. And that unblocked everything.
I still do not understand why the other sites are causing problems. But in my opinion I am good to redo a wp config.php on each one to unblock everything (if of course the problem comes from there).
Thanks again for the qualitative response (sorry my english so bad :p )