Oh ! 
I was trying one last setting before giving up …
I activated “Download MMS automatically” and… it worked ! (at least for an MMS sent to myself, I can’t ask someone to send one at this hour) 
Its really cool, but could I find info why it’s not working without this ?
I still can’t retrieve past MMS and that’s why I would like to make it work both ways, in case I receive MMS in a “no data” network zone, I’ll have the notification but won’t have the file.
I’m sure the timeout is the key, but I don’t understand why would it make a time out when retrieving manually and not when it’s automatic 
Thanks !