Yes. Using a shift register to add output pins is common practice. The shiftOut() function will help. You'd use the ShiftOut() twice in the main_write_DATA() function to send the data to your shift register.
I cant understand from the tutorial what to connect to the arduino.
in my chip, there are some extra more function like the r/w and the SHCP and the STCP.
Can you please help me with some diagram?
SI - serial input (I get this)
CP - active low (ground)
Witch pin goes where?