You say that the trusted actor updates the public key of a coin. This means that it is known which former key corresponds to which following key. Thus the central actor can trace the history. If you have many trackers, then everyone can trace the history.
Yes, but it only knows the public key. Which is not a number in any way associated publicly with the identity of the owner...it's essentially a (discrete exponent of a) random number that identifies the coin.
