Re: Gemma and NeoPixel problems after short circuit
Just to check: the device in the picture is a Flora not a Gemma. You said you don't have a good photo of the Gemma, so am I right in thinking you connected the Flora to show how the NeoPixel ring looks?
If that's correct, you can test your Gemma by loading a simple "blink an LED at 1Hz" sketch into it for each pin. Two or three voltage dividers and `analogRead()` will tell you whether the ADC is working correctly, and a voltmeter will confirm the outputs from the Vout, 3.3v, and GND pins.
WRT the ring that only lights part-way, it looks like the first non-working NeoPixel is dead.
NeoPixels use a rather neat communication protocol: each chip consumes the first 32 bits of input it sees on the data line, then copies everything else to its next neighbor. That makes life easier for a logic device controlling a string of them, but if one chip dies, the rest of the string loses its data connection.
WRT the all-white output from a strong power supply, does that happen with both rings and when running from both the Flora and the Gemma?
When you void a product warranty, you give up your right to sue the manufacturer if something goes wrong and accept full responsibility for whatever happens next. And then you truly own the product.