Are you using the Teensy 3.3V regulator output to power a lot of peripherals?
There has been some evidence that hanging large amounts of capacitance on this output can sometimes cause reverse current flow through the regulator during power...
The diode is a reverse voltage protection diode, so it would be placed so that the cathode with the line is on the right towards the regulator.
I don't know anything about this board, but it doesn't sound like you got the right board. The last...
Yes, you can power a project using a portable charger like that through the USB on the Teensy. It won't hurt anything as long as total current is kept below about 500mA or so.
Cutting the VUSB trace is done if you are supplying an external...