If you go the form 1 route to register your lower as a SBR you become the maker of the SBR and you add your name and address ie John Doe Boston, MA. If you go the trust route it would say someting like The revocable living trust of John Doe. Boston, MA.
No you can not make a machinegun for private sale. You should read Scotty Ryan's sticky how to SBR your lower.
http://www.m4carbine.net/showthread.php?t=9830
He covers the topic well and if you ask questions there lots of other folks will see it and may reply with helpful info.
You don't need a trust it is just an option.