Thank you for the answers. Yeah, now I know that I don't need the CTS, RTS signals. On the arduino board I have a 5 V signal, so I don't have to convert the 12 V into 5 V from the PC RS-232 port. For the full-duplex connection, I guess I will need two SN75176 IC-s and some resisters. I almost know the connections but the thing what I don't know is how to control the IC-s and the direction of the data flow.
Thanks!