If (and you should) download another browser such as Chrome or Palemoon make sure you make it your default browser, Other wise you'll be stuck having to use IE.
You can always change the setting.
That never changed how Windows Update worked on XP, it always uses IE.
And if you copy/pasted the URL for Windows Updates into Firefox, there was an error saying you had to use IE.
I'm not sure what you're referring to. If you mean manually finding and identifying and downloading and manually installing updates, yes of course that can be done with a non-IE browser. Hell, I've done that with Firefox on Linux.
I'm talking about the normal Windows Update service that normal users use, to get Windows Updates.
How were you able to run the Windows Update service with (say) Firefox?