need more information what operating system? Version? How did you install Firefox? Portable version? That version is not installed and will not show up in the Windows start menu

"firefox disappears from my computer" What do you mean by this? Is the icon disappearing from the desktop? if yes, have a look in Start - programms

You can check in Windows explorer - Programm Files whether there is a folder called Mozilla Firefox. If yes, you can get the Firefox shortcut from there to the desktop

Are you sure you installed Firefox properly? https://support.mozilla.org/en-US/kb/how-download-and-install-firefox-mac

Also are you sure do not have something that reverts things to a set state?

I have a Macbook Air that's a couple of years old. It works fine for many days. It's in the menu bar at the bottom and on my desktop. BUT, when I shut Off the computer and restart it, It disappears. From the menu bar, the desktop and in the Apps folder!?!?!

Unfortunately I'm not familar with Mac, but you could try to install another application and see what happens with that. Maybe it a general problem with you Mac that affects all (new?) applications. If yes, then you may want to post this in a Mac Forum, in the case nobody here can help