MerryMarigold - Garlic, so are you saying the satellite pings likely held more info like altitude, fuel etc. re your post at 4.53.
We know the satcom is equipped to relay detailed information about the engine's state to Rolls Royce. We know Malaysian subscribed only to the basic service, so did not receive engine updates. We think RR probably collected this data anyway, for its own technical use. We inferred that this is the information Inmarsat said it shared with its 'partner' and was working to extract.
If they have got the engine updates, they'll know a heck of a lot about what the plane did. As it wasn't subscribed, though, it might have gone into an anonymised stream of data which would then have to be painstakingly pulled out.
is it known whether the plane could "ping" from a part floating on water
Lovely idea, but no. The engine has to be on, to power the antenna.