uhm... The Vajra taught her it? The Queen on the Global specifically? How do you usually learn a song from someone?
Got the disease from 'hanging' out with the queen? If I were to speculate (oh how sinful of me), the Queen might have deliberately infected her to as an attempt at communication, as it'd allow her to hear fold waves, not knowing it'd prove fatal. I think I recall Grace saying something like "Why do you keep covering for that thing, even to the point where it gave you that" with regards to her illness.
Uhm, by doing bad things to them? Does it matter? You're making it to a much larger deal than it needs to be, raging over the plothole when in truth we don't need to know what happened exactly. Knowing more would be nice, but it doesn't cripple the show not knowing.