Macos: prevents Safari from leaving the full screen of the movie

Suppose I am watching a YouTube video and I make this video full screen by clicking on the full screen icon in the video. I am not talking about Safari in full screen. I am talking about the video in full screen.

I have 2 external monitors.

I click on the mail icon in the second monitor document, waiting for the mail to open on that second monitor.

When the mail is opened, the video goes to full screen but continues to play without an image and the safari shows that annoying message "press ESC to exit the full screen".

Two things:

  1. Is there any way to prevent the safari from doing it?
  2. Is there a way to open an application on the monitor from which it was called?