Regarding your original question: "When a user tries to establish a connection to Teradata, will Teradata Gateway receive and send that request to any 1 NODE?(if yes, on what basis)"
Sessions are owned by PEs. At logon time, the Teradata Database Gateway chooses a PE for the session. Typically, the Teradata Database Gateway will choose the PE with the fewest sessions. The chosen PE may be either on-node or off-node with respect to the Gateway.
Regarding your original question: "When a user tries to establish a connection to Teradata, will Teradata Gateway receive and send that request to any 1 NODE?(if yes, on what basis)"
Sessions are owned by PEs. At logon time, the Teradata Database Gateway chooses a PE for the session. Typically, the Teradata Database Gateway will choose the PE with the fewest sessions. The chosen PE may be either on-node or off-node with respect to the Gateway.