Is it possible to do some echo on
/dev/ttyS8 serial device in one terminal window, and in second to cat
/dev/ttyS8 and display data from that file?
If you stick a serial loopback adapter in the specified serial port: Yes.
If you want to debug an application talking through a serial port, you could use this socat command:
socat /dev/ttyS0,raw,echo=0 SYSTEM:'tee input.txt | socat - "PTY,link=/tmp/ttyV0,raw,echo=0,waitslave" | tee output.txt'