given that Yggdrasil is just an IP network, I can't see a reason that in-Yggdrasil email would be a particularly complicated affair - though it may have to be on a separate domain (and that possibly in a separate domain-name system, which I'm aware the augúst administrator of this site has involvement in), to avoid conflicts with outernet senders who don't know about Yggdrasil.
Yep, you are right.
We just can forget about STARTTLS for SMTP (Yggdrasil has an encryption level) so we can forget about certificates from CAs. Then, we can use ALFIS domains or even OpenNIC and such for domains.
See https://fedoramagazine.org/decentralize-common-fedora-apps-cjdns/ for examples with linphone and opensmtpd. It uses Cjdns - but yggdrasil works the same.