1. I'd go for MDF and 2 layers of 5/8" gypsum with Green Glue between the layers of gypsum. You'll get better mass at less cost.
2. Mineral wool is just as efficient as pink fluffy, AFAIK... and cheaper in many parts of the country.
3. You DO need a vapor barrier.
4. I would slip it between the studs, and then tack up banding material to hold the insulation in the bays.
5. I can't comment on the Auralex, but if the absorbtion numbers are about the same (which I suspect they're close), then go for the cheaper cost item.
To save some more funds, I would leave the floor untreated and put in a soft ceiling... easier to keep clean and more natural sounding.