This guide shows how to wire the screens too:
Red will go to 5V power, black will go to the GND rail, and yellow or white (not both) will go to the TV pin on the pi zero.
viewtopic.php?f=22&t=958
As for your powerboost wiring, I would wire the red and black coming from your power strip to the pp1 (5v) and pp6 (GND), below the power usb port.
Not sure why the battery isn't charging. When you plug the battery in does the orange charge light come on?
As for the switch, if you are using the powerboost 1000C I think you just need two wires. the EN and GND.
Audio stuff, here is the diagram I have made for my setup:
Purple is audio out from the pi's GPIO pin, I have wrapped it with a ground wire to help reduce static. The yellow wire is the output pin of the volume wheen, which goes to the amp, I have also wrapped it with a ground wire. You are using a different headphone jack but it should work pretty close, have a look at this link:
viewtopic.php?f=22&t=701
Your jack is the last on the list, and it shows what each pin does. I think your headphone would need to have '-' from the amp to '1' on the jack which then goes to the speaker, and the '+' would go to '2' or '5', and then from there you would wire '3' or '4' to the speaker...
you dont need ferrite beads or resistors, but they may help. You can also use a low pass filter to help reduce static.
Now, to wire your external USB, green and white (D+ and D-) will go to the pi zero pp22 and pp23, and the power and ground will go to your power strip.
Micro USB will be wired to the USB and GND on the power boost, you do not need to wire the D+ and D-
I tried to answer as best I could!