Note that at least during this development period it is important that your version of Firebug be synchronized with your Chromebug version.
To start Chromebug then firefox use:
To start Chromebug then thunderbird use:
The Console, HTML, CSS, Script, DOM tab row shows the data for the nsIDOMWindow selected by the "context" menu. So for example if you set the context to browser.xul, the HTML you see will be the HTML for firefox's window.
Most of the time you can just use the context menu to set the tabs to the content you want to explore.
Or you can use the inspect feature to select the context.