Hello altitudeap,
Sorry for the late reply, I have been on holiday 
For instance, when I am viewing the debug, and I am moving from page0 to page1, I get an simulator output (I am assuming I will see this as a serial string?) of "65 00 02 01 FF FF FF"
Yes, what you see in the simulator window is what is sent to the Nextion serial port. I would hesitate to call it a 'string' as that words has specific meaning in the C and C++ languages, and I don't think this data qualifies. Those bytes, as shown in the simulator window, will be sent to the serial port.
It is clear from the rest of your question that you have not tried my examples as set out in this tutorial, the answers are in there. Try the examples, then come back when you need further explanation.