The next ping will give us another arc, the difference between arcs reflects the distance traveled.
Nope, because you don't know what point the plane was on for any of the arc.
All you can tell by consecutive arcs is what component of the track was toward or away from the satellite.
If you know the speed, then using simple geometry, you can then calculate the other component, and that will then give you a position relative to the previous ping.
I assume this is how the NTSB decided on the location in the southern ocean.