"And now put in your precious window the setting "hide the taskbar" and find me at least one player in which you can put the video to pause from full-screen mode without using hookies";

I don’t know where the discussion started, but:
Media Player Classic - double click - turn off/off full-screen mode, single click - pause,
VLC - double click - full-screen mode, pause (in full-screen mode) - in the pop-up panel or in the context menu.
The default windows media player (if anyone is using it at all) is similar to VLC.
You need a panel of tasks and wishes for this - I can't understand more.