As far as I am aware that HS servers need to communicate with 3 points, which are Introduction point, Rendezvous point, and HS directory. So how many Tor relays are there in the circuit between the HS server and these 3 points?
Each Tor circuit has 3 relays: a guard, middle, and exit. A HS server will build a Tor circuit to the Introduction Point, Rendezvous Point, and HS Directory, so there would be 3 relays between the HS Server and any of these 3 points.
When browsing a Hidden Service, your browser and the HS Server each build their own circuit to the Rendezvous Point, so there would be 6 relays between the HS server and client, 7 if you count the Rendezvous Point.
The Hidden Service descriptor is signed with the HS Private Key before being sent to the HS directory. According to the Rendezvous spec 1.4,
Upon receiving a descriptor, the directory server checks the signature, and discards the descriptor if the signature does not match the enclosed public key.
It doesn't specifically say if the descriptor is hashed or encrypted, but if it's signed with the private key, the public key can be used to verify authenticity. The Public Key is then used to encrypt messages to the HS Server, which can then be decrypted with the Private Key.
The Rendezvous Spec talks about encryption in various parts, but it seems to be talking about the actual rendezvous and introduction point, not the HS descriptor.