Is any way to programm Arduino through some of his other serial ports like RX1 TX1 or RX2 TX2? If it exists, can someway give me some guidance?
Yes, this is possible but it needs a fair amount of learning and time to do the programming.
You can adjust the bootloader of the Mega2560 to use another serial port than the first one. The bootloader source code can be found in the following subdirectory of your IDE installation:
hardware/arduino/avr/bootloaders/stk500v2/
You might have to adapt some paths in the Makefile to match your installation. Changing the source code to use another serial interface is not too complicated but needs knowledge about the datasheet of the ATmega2560. Adapting the bootloader to listen to more than one serial interface should be possible to but need far more changes to the existing code and indepth knowledge of the AVR startup process as you might have to adapt the bootloader size.