Wow, you've given me a load.
In most modern SoC (system on chip) you're got a couple of hundred pins or contacts
Connections are at a premium so you want to keep that number down.
But a chip is expensive to design and it might get used for lots of different usages.
Somebody might want a LCD display with a good 20 pins. Somebody might have no need of a display.
So what you have is that any modern SoC has a "Pin Mux".
Usually that means that every single pin can be a GPIO. Some of these pins could be UARTs. Some of them could be I²C.
Let's say that you need a UART. There could be 6 UARTs built into the SoC.
You look at the documentation (hard to find sometimes) for your chip.
"Well, what if I take UART1? I can assign that to pins 25/26 or 90/91 or 124/125. Oh, wait, I'm already using pin 26 to drive the charging LED and 90 is part of my SD card interface and I've got the keyboard connected in the 125 group. Guess I'll use UART2 instead. Of the 4 possibilities for that pins 62/63 are entirely clear."
So the Pin Mux is like a switchboard for connecting functional units inside the chips to pins that connect to the output.
Unfortunately, switchboards are very expensive (in terms of silicon real estate) so we don't make it that you can connect anything to any pin.
But hopefully they give you enough possibilities that you don't get too wedged designing things.
Another job of the Pin Mux (really the Pin Pad configuration) is to set whether a pin is an input/output/both, how hard it drives an output, whether an input has resistors to pull it up or down and for some chips whether the pin works on 1.8V or 3.3V logic levels.
As far as test points go. Most circuit boards have tiny gold dots that allow for connection for testing.
For instance, you want to be able to test if the board will power on without the little button board for the power switch connected.
So they put a little dot that can be probed by a "nail" or "pogo pin", a spring-loaded contact.
You'll probably see a group of three of them around the VolUp/VolDn/Power.
The power button has to wake the device from full off, so it may be wired differently than buttons that only have to work when it's on.
You're telling me that you're measuring 3.7V on a resistor that goes to the power button?
That seems to be the full LiPo voltage. When you press the power button you see no difference in the voltage from either end of the resistor to ground?
If you can, take a good high-res photo of the area right there.
Most modern Androids do OTG just fine (with an OTG adapter).
There can be problems if the peripheral is looking to be supplied with too much current.
You can use a hub on OTG. The "input" goes to the OTG adapter, one of the "outputs" goes to the peripheral.