Can I send / retrieve MMS messages via WiFi? Is it possible to send / retrieve MMS messages via WiFi or is it mandatory to be connected to my provider via the mobile data connection?

If a user has an active WiFi connection, what happens when there's an incoming MMS?
It could be done technically. AFAIK all communication between MMS enabled components is done via standard TCP/IP.
But in a regular provider setup the MMS store and forward server(s) (MMSC) are only reachable via the providers network. That's why you can not send and receive MMS via WiFi.

It's also the reason why you can not make a call and send/receive an MMS simultaneously when you have only 2G (GPRS/EDGE) connectivity.

Normally android will drop the GSM data connection if there is WiFi connectivity and all data will be routed through the WiFi interface, but there is one exception: The MMS traffic will still go through the mobile data connection.