How to start using installed Firebug

What kind of redirect? There are Firefox addons outside of Firebug you can use to stop redirects. Firebug does not seem to provide this functionality itself.

Redirects based on the HTML "Meta refresh" (also HTTP "Refresh") can be blocked by setting accessibility.blockautorefresh to true in about:config. In fact, this corresponds to the "Warn me when web sites try to redirect or reload the page" option in Options > Advanced > General. Alternatively, addons such as RefreshBlocker can be used.

For JavaScript based redirects, JS can be completely disabled or addons such as NoScript can be used.

There generally isn't much you can inspect on a page that is redirected using HTTP 3xx response codes. In case anyone wants to know, setting network.http.redirection-limit to 0 in about:config causes all of these to show a Firefox error page.

JS redirects

JS-based redirects are difficult. I'm not aware of a method to stop them from within the browser. However, you can intercept the responses with a debugging proxy like Fiddler2, and replace it with your own modified response (the AutoResponder in Fiddler2 is one way). In this modified response, you'd want to remove any references to window.location and location, the usual ways to change the page from JS [you might be able to get away with replacing them with a dummy variable, e.g. var thisIsAMadeUpVarName]. That way, the redirect would never get to the browser. See the "Search and replace in HTML." section of this document (you may wish to also filter JS files if they are served separately).

The broken Script panel is obviously a known issue related to Firefox 50.0+.

Though as written on the Firebug homepage, the development and maintenance of Firebug are discontinued.

Instead, Firebug users are advised to switch to the Firefox DevTools (which now provide a Firebug theme to make the transition easier). See also the related blog post