I have three computers connected to a router at home. I am sure my router has only one address. When the packet arrives from computer 1, the source IP is translated to the router IP address. 

Let's say both computers 1 and 2 access the same destination, this time the entry in the NAT will have the same destination address. So, how is the packet forwarded here? 

When the packet arrives from destination, how are the packages distinguished between computer 1 and 2? I have a Belkin router, is it generating many source addresses. For example, dynamic NAT, each source IP is converted into a different IP address? How does it generate a pool of addresses.