1. Trying to join a group from a banned domain: If a domain is banned, then if someone with that domain tries to join the group, they get a message to the effect that people with that domain can't join the group. (Note that this is different from an individual email address being banned. In that case, the person, if logged in, cannot even see the group's home page - if they try to visit the page, they are confronted with their list of groups and a banner saying "you are not in this group." They can't join via email either, but I'm not sure of the exact message they receive in that case.)
2. Sending messages from a banned domain: If someone can't join a group because their domain is banned, they're not in the group, so messages from them to the group bounce just like messages from any other non-member.
I can't answer the rest.
Messages are the sole opinion of the author, especially the fishy ones.