I didn't check that all your numbers are correct, but they seem reasonable. Tor clients try to use three relays of its own choosing for anonymous circuits. Since the onion service chooses the introduction point, it only needs two other relays before it. Similarly, since the client chooses the rendezvous point, it only needs two other relays before it. In all of these cases, the circuit contains three relays chosen by the client.
Also, I saw that in the connection establishment scenario with a normal web server, the client - Directory Server connection has only 1 hop/node? If this is true why does the HSDir connections have 3 hops in between?
Connections to directory servers don't have 1 hop in between. Rather that first hop is the final destination. These relays are generally directory caches, so the clients download the directory documents directly from these relays. This is because the clients don't need anonymity in this case. Everyone downloads the same directory documents, so the server should not learn anything about the client (other than the client's IP address) or the websites that it visits. Tor clients use directory guards so that only a limited number of relays ever learn the client's IP address.
Hidden service directories act differently. Unlike directory documents where all clients download the same documents, clients request individual hidden service descriptors depending on what onion address the user attempts to visit. In this case the user requires anonymity since every user will request different combinations of hidden service descriptors.