What could be the maximum number of concurrent Clients (using different port number) that could communicate to a Server on the same port (Single socket) ? What are the facto
More than you care about. Or rather.
I can guarantee that it is more than all of those. There are scalability limitations with large numbers of sockets, which can be worked around (Google for the c10k problem). In practice it is possible to have more than 10,000 sockets usefully used by a single process under Linux. If you have multiple processes per server, you can increase that up again.
It is not necessary to use a single port, as your dedicated load-balancers will be able to round-robin several ports if needed.
If you are running a service for many 10s of 1000s of client processes, it is probably fairly important that it keeps working, therefore you will need several servers for redunancy ANYWAY. Therefore you won't have a problem deploying a few more servers.