Octane, if your ISP provides it, you can log in to the ISP webpage and retrieve emails via a browser (Firefox, IE, whatever).
Most ISP's provide that, here, where it is called webmail. (and possibly also called webmail internationally...I don't know.)
Go to your ISP's homepage, log in (usually a "members" or "users" tab somewhere) and see if it is available, or phone them and ask. It should be pretty straightforward.
Once you're logged in, accessing your emails - that would normally be accessed by your email program (T'bird or OE) - is just like using the browser to access hotmail etc.
You can't use T' bird/OE to access Hotmail. It's designed for a browser.
Not a Skype user, but some external applications don't give the option for using a different browser for updates. Ask Skype about it, probably on the forum. (Bound to be one.)
FF with the IE extension can process M$ updates. But I've never bothered. Just use IE, for updates only. My computer has FF as the default browser, but if I click the "windows (or ms) updates" function, IE automatically opens.