How would that work? First of all, the clients need to know which exit nodes exist, so that they can build circuits. That list, as well as that of the middle nodes, is public, otherwise you'd >have to manually request exits by email/web service/… As a result you'd be limited to a few exits, which might not necessarily have an exit policy matching your needs, or might be offline, >or simply overloaded on account of there being less than regular exits.
The same way bridges work. They are not published.
See the answer by Matthew about that, apparently that question has already been answered in the FAQ.
By the way, I just checked, Gmail works without problems over Tor (both Web and IMAPS).
Using Gmail over Tor when they already know who you are is self-defeating. Try to register an anonymous Gmail account using Tor.
Doable. They require a phone number for verification, but that's the same with and without Tor. Besides, if you want an anonymous email, use _anything but Gmail_, eg. ProtonMail.