Yes, of course. Like all other settings. Have a look at the table egw_config.
No idea.
Does that apply to other settings in your case as well?
What happens if you do not restart the server at night (Is it really the restart?)?
No.
This definitely does not happen with me. We have no other reports on this either.
Is it written correctly into the database when you set the setting?
You can test with 2FA for example:
Stefan