When a client connects to the server, one socket.
When another client connects before the server has finished with the previous, another socket.
When you connect to a server as a client, another socket.
That is three sockets used. One remaining.
edit: My bad. I forgot the second question.
As each connection is closed properly, the socket is freed up for another connection. This applies to both server clients and client clients.
This is why I already have the library code ready for the w5200. It has 8 sockets.