The detail will depend on the make and model of the router, but this is the general information.
The Network B will need to connect to another interface on the router.
The router is already configured to translate the addresses of Network A to the fixed IP address given by the ISP. A similar configuration will be needed to translate the addresses of Network B to the sam fixed IP address.
It will not be possible to translate any port coming in to a specific PC on network B. This can be done for some ports, but each one will need to be defined. If you do it for all ports, you are likely to stop the outgoing traffic translations. It is also not good practice to translate all ports, it can make your network vulnerable to attack, restricting it to specific ports, makes this much safer.
Stopping the two internal networks accessing each other is just configuration on the router. On Cisco these are access lists (ACL), if your router is a differnet make then it may be done in a different manner.
If you can post the make and model of the router, that would help to give a better answer. If you can also post the configuration (remove any passwords, and change the fixed IP address) then we can help more.
I hope this does help you, at least a little bit