1) They will not be able to detect if their key has been changed by the identity provider. 
As a result, the identity provider can change the public key of this user to an attacker controlled public key in whichever epochs it wishes to do without being detected.
2) (a) Identity providers learn the public keys of users in the system, and learn which usernames are looked up by a given user.
   (b) Clients cannot learn anything about the key database beyond that revealed by queries. If you query a username, you learn if it exists and its public key. But with the VRF design, you do not learn information about the neighbors.
   (c) Auditors cannot learn anything about the key database beyond that revealed by queries.