I'm not sure of any details but I believe that the aircraft's engines were each also supplied with telemetry radios that were independent of any of the on-board and crew-accessible systems, and these continued to send out position updates even after the other telemetry stopped.
It is difficult to tell anything for sure, as there has been a lot of conflicting information regarding this flight. Malaysian airlines has an abysmal safety record but if the plane had simply crashed I think we'd know more by now.
Yes - Rolls Royce receive telemetary from all of their engines that are in the air at any time. I guess they would be able to tell if the plane was flying but not necessarily where it was.
Which they receive via ACARS - which was switched off.
The engines have their own telemetry transmitters as far as I understand it. I don't think they use ACARS.
Then your understanding is incorrect.
The engine systems feed, along with other airframe systems, into the ACARS system. ARINC are responsible then for disseminating this to the end users, in this case Boeing and Rolls-Royce.
With the ACARS unit off, but the INMARSAT terminal on, the terminal remained in periodic 'keep alive' contact with the satellite. This is like your switched off mobile periodically contacting the local cell to maintain its cellID.
I can foresee a future change to the INMARSAT protocol that ALL transmissions must, where available, include positional data. This would be a simple firmware change and would be a cheap way for the aviation industry to help negate this sort of incident in the future.