#1 already exists in the form of S/MIME, which uses the same kind of certificates as SSL and TLS do. Problem is, the certificates cost money (with the exception of StartSSL's) and basically all webmail clients don't support them.
(Aside: It does make sense why webmail clients don't support sending S/MIME email, but I'll never understand why they refuse to do something useful when they receive a S/MIME signed email. If they did, that could pave the way for something akin to what EV does for the Web, so that I could look for a green bar that says "this email is signed eBay International AG" and know I'm not being phished, for instance.)