Since I am not CfB, I cannot guarantee that my answer aligns 100% with his vision but this is my understanding of it:
1. Functionality of distributed coordinator in Cluster 0
Yes, exactly. The entities don't have to be companies, but it's very likely, that they will be.
2. Need of coordinator(s) in other clusters
I don't know if Cluster 0 will need a ...
Initial motivation for checkpoints in bitcoin is to prevent 51% attacks as explained by satoshi (July 17, 2010):
The security safeguard makes it so even if someone does have more than
50% of the network's CPU power, they can't try to go back and redo the
block chain before yesterday. (if you have this update)
I'll probably put a checkpoint in ...