Firstly, forgive me, I know I've seen these explained somewhere but I cannot find a source anymore.
I THINK they mean the following:
Color - 32-bit ARGB pixel format with alpha, using 8 bits per channel.
DXTCompressed - DXT compression (https://en.wikipedia.org/wiki/S3_Texture_Compression)
NoChange - As the texture is imported. So if its a PNG, it will export as a PNG and then load uncompressed into memory when the game runs? 32 bit? (This assumption seems wrong after playing around with it. Not sure what this setting is for)
Color16bit - Bgra4444 16-bit BGRA pixel format with 4 bits for each channel.
ETC1 - Ericcson compression (https://en.wikipedia.org/wiki/Ericsson_Texture_Compression)
PVR - PVRTC (https://en.wikipedia.org/wiki/PVRTC)
ATC - ATSC (I think??) (https://en.wikipedia.org/wiki/Adaptive_Scalable_Texture_Compression)
Compressed - No idea. I think I read somewhere it was platform dependent
Secondly, is there any side effects to mixing compression types?
Lastly, it would be great to add these definitions to the official documentation. If I compile them, can I add them to http://www.monogame.net/documentation?