Instead of getting my numbers in the serial monitor, I receive rubbish (attached image).
Pin18(TX1) , Pin19(RX1) and GND of the board are connected to Prolific USB-to-Serial Comm Port Adapter.
The connector pin assignment of my (male) 9-pin serial adapter:
Serial Pin5 =GND
Serial Pin2=TX1 (18) of MEGA
Serial Pin3= TX2 (19) of MEGA
I don't know what device you are sending that to, so it is hard to tell what your problem is. If you are using the serial monitor on the Mega2560, then you should get nothing (or garbage if you did not initialize Serial). The serial monitor is connected to Serial, not Serial1.
I thought this adapter (picture attached) is doing the work to change the signal to rs232 standards? I wired the serial side to my board and the other usb side to my pc.
Please correct me if this doesn´t work
If that is a usb to RS232 adapter, then it won't work. Your Arduino serial port is NOT RS232. It is TTL! You must get the correct adapter of use another adapter to convert from RS232 to TTL serial.