As the title states, I would like to know whether one could create a smart contract on Ethereum that is able to send and receive E-Mails.
If you are perceiving emails as data transmitted over classical protocols stmp, pop3,etc the answer is No it's impossible. As you might know, the smart contract runs in an isolated environment (VM) it has no connection with external networks.
So a smart contract can't connect to an stmp server and send an email to firstname.lastname@example.org
A contract can receive "transactions" which can play the role of emails !!