Storing them in IPFS is not storing them on chain, you might actually lose data if the IPFS nodes don't pin in enough locations and the modes that fid leave the network
Then that's not an "email service".
Okay, you can call it a messaging service then. I don't think spending time on nomenclature is worthwhile; and "email service on the blockchain" would be clear enough for most :)
No, because people will expect to send emails to other people who do not use your system, and also get emails from them.
Email is already a protocol, you are creating a different system.