Does Arduino due allow you to upload a program on programming port and then run it through Native port?
You don't run a program through anything. You run it on the Due. Where you send text to is entirely up to you.
Can I work with SerialUSB instance in Programming port?
I have no idea what you are asking there. Both the Programming port and Native port are capable of being used as virtual USB COM ports. They use CDC/ACM. One is directly connected to the SAM3X chip's USB peripheral, and the other is connected to the SAM3X's UART interface via another microcontroller as a USB to UART converter.
lack of info on the net about it
Then you can't be looking very hard. – Majenko Feb 26 at 10:22