Yes; for instance you can open New Private Window and login to the second hotmail account.

No, that is no way to do it, because of the already logged in *@hotmail.com account window opens, and if you log out only then can I open the the other *@hotmail.com, As far as I can see there is no way to have two different *@hotmail com open simultaneously with Firefox, but I would love if you could prove me wrong.

I think hotmail.com would detect the browser and see they are both FF but if one is FF, Edge or Chrome or IE11 should work. I done that before yahoo in FF and yahoo in IE11 without problem.

Thus far that is my opinion as well. I have used the IE with the other hotmail account, but the IE started to act up, by not saving the sent emails and I always have to Bcc to myself and that is not the best way to store emails (questionable proof as well). I wait for a while perhaps someone comes up with another idea, then if that is not going to happen I download Chrome and start using that wit the other hotmail.

The Containers add-on from Mozilla is exactly what you are looking for. Perfect for this use case

https://addons.mozilla.org/en-US/firefox/addon/multi-account-containers/

Yes! - And Thank You! I had difficulties to set it up because you cannot use it if the browser set to private browsing mode. The setup page does not warn you, however after some thinking I figured it out. Thank you again!