I was reading a lot about nodejs but still not clear about following :
With TCP protocol client and server agree on one port and then can maintain a connection.Server knows IP address of client and hence can send back messages.If we use nodejs then multiple clients can connect to same nodejs server on same port. How this can be possible? How multiple connections can be established on same port by same server.
There is no limitation to the number of connections which can be maintained on a single port (although, in practice, there may be operating system or hardware limitations). Of course, only a single process can listen on a port, but that has nothing to do with connections. That's not node-specific, all TCP servers work like that.
If client is behind NAT then its IP can be dynamic , so how can nodejs server can send data to client.
You're essentially asking how NAT works. Again, there's nothing node-specific in this case. The NAT server simply alters packet headers as necessary, and maintains translation tables for routing, just like with any connection.
What will be resource utilization in maintaining persistent connections on server and client
The overhead is really quite minimal for just the connection itself. A little bit of memory, but almost insignificant in the big picture. If you're storing additional associated data with each connection, that may be different. Node.js handles large number of concurrent connections very well, but if you're concerned, you can always search for benchmark tests, or write your own.
What happend when nodejs server crashes?How can client initiate connection again?
Sockets emit both close and error events. Simply listen for them, and attempt to reconnect afterwards, probably with a back-off delay.
If there is network problem on client side and it terminates and initiate connection after every 5 mins ..then is there a way this scenario can be handled?
Not entirely sure what you're asking here. The client simply needs to reconnect as stated in the previous question/answer. If you're associating certain data with a client socket, and you want a grace period where the client has a chance to reconnect before that data is freed, then you'll need to set a timeout which will free those resources after a certain amount of time. Then, in the connection listener, or perhaps on an authentication event, you'll want to analyse the new connection to see if it matches a recently disconnected client.
I would definitely recommend looking at socket.io, especially if your use case is web-based, although it can be used for more than just browser/server connections. It will do a lot of the things you seem to be concerned about (reconnection, resource association, disconnect grace period, etc) more or less automatically.