Can two computers communicate by connecting each other using an Ethernet cable back - to - back?

Yes. This can be done with what is known as an Ethernet Crossover Cable. Connecting the NIC of one computer to the other. The cable can be bought or made and a quick search will show you a diagram of how it is wired. Basically the send and receive pairs are reversed on one end so that the send output signal goes directly to the receive input of the other and vice versa.