Hi Budvar,
The serial connector is labeled serial ouput. It's not the memory key or the keyboard connector.
The USB307, it doesn't do a lot for the price 
It has two important things a max232 chip and a ftdi chip.
If you do as pictured in the second picture, you'll be able to see the bytes from the serial output. Use a ttl to usb cable and your computer will be able to use terminal, screen, minicom or any other terminal communication tool...
I'll use the computer until a understand the protocol and will transfer the serial communication and analysis to the arduino.
And yes, you don't use the power from the serial output, use the 5V from the usb cable. On the serial output connector, the pin you will use is tx, rx and gnd.