Your questions are too comprehensive for this forum to answer in detail. Microsoldering and electronic repairs are a lot different to screen replacements. From your questions I would suggest maybe enrolling in some kind of hands on learning course.
This board you have “820 00045” is not what you want to start learning on. A more appropriate board would be a 2012 MacBook air.
I will endeavour to answer some of your questions.
· Most repairers have more than one power source and device to easily check the power source is functioning. Another way to check in your situation would be to check the voltage at the board connector.
· There should be a dedicated page on the schematics called power rails or power aliases. Depending on what the board is behaving like depends on what power rails to check. In your circumstance you would start at the top. Why you would want to check pp3v3r3_aon when your USB read out is showing 0V?
· Checking the power rails to ground with a multimeter will tell you they are not shorted or partially shorted to ground. It will not tell you why it is not getting power when it should. Power rails can be checked on Caps Resistors, Connectors and IC’s it doesn’t matter.
· To understand schematic drawings you need to know what the different components do and what there symbols are. You need to research.
· Capacitor
· Resistor
· Diode
· Transistor
· Voltage divider
· Buck converter
On top of this you will need to learn microsoldering.