The Arduino has only one UART, so it can't act as a bridge between the computer and the Blu-Ray. I don't speak Polish, but from what I can tell on the site you'll have a lot more luck just using an FTDI USB->serial cable and connecting to the header. I recommend the TTL-232RG-VIP-WE from FTDI, found here: http://www.ftdichip.com/Products/Cables/USBTTLSerial.htm
This is a wire-ended cable, so you'll need to attach some sort of header to it to be able to interface physically to the Blu-Ray, and you'll also need a connection to VCC and ground (so the cable can detect the proper voltage levels). Then you just have to make sure that the computer's RX is connected to the Blu-Ray player's TX and the Blu-Ray player's RX is connected to the computer's RX. Then use a serial terminal program to connect and go crazy.