To switch between Firefox windows use: (Shift) Cmd + ~ (Tilde)

See also:

• http://www.danrodney.com/mac/#windows
• https://support.mozilla.org/kb/Keyboard+shortcuts

I have a mini keyboard, don't see tilde sign, and many others like "home" , "end" etc

Does it have a accent key (`) that you can use instead?

yes it has. What command should I use ?

Does that ` key work in combination with Cmd and possibly Shift?

Plz stop your nonsense

All articles state that cmd and ` or ~ should do this.

• http://support.apple.com/kb/HT1343 OS X keyboard shortcuts

Check that you've enables this switching.

• http://support.apple.com/kb/PH4182
• System Preferences > Keyboard > Keyboard Shortcuts > Keyboard & Text Input:
  "Move focus to next window in application" should be checked.

It is set as you suggest, but I cant switch between windows or tabs with keyboard shortcuts

Maybe it is best to ask advice at a Mac oriented forum as they know much better how to deal with Mac specific issues.
I'm on Linux, so only can pass suggestions that come up via a Google search or from past encounters of this issue and your computer seems to behave differently because that key combination used to work for others who previously posted about this on this forum.

I did that, it is restoring the app tabs as long as I do not restart the computer. But when restarting - it is all gone- Besides I also often get messages on script error, which maybe is not related to app tabs FF is also very slow to start. An alternative to App Tabs is Zetero. Do you know anything ab that ?

App tabs may not be restored if you first close all Firefox windows, but still have Firefox running with only the menu bar visible and let the Mac OS automatically quit the Firefox application when you close down the computer.
App tabs are connected to a specific window and only if you use "Firefox > Quit " to close Firefox with all open windows then the App tabs are stored correctly in the sessionstore.js file and restored on the next start.

the Keycut (shortcut) for switching windows on a 'Toshiba-Satellite L840 is: Alt+tab

I have Mac Mini ; your suggestion does not work. WIndows machines allow "side by side" view , which I am missing here on Mac

....finito la comedia....