"How do they know the water is everywhere? How do they know it's not just in the one place they dug and nowhere else?"
Mars is believed to have a global soil layer, due to massive windblown dust storms. The area sampled is specifically chosen to be this dust and not local soil.
"Why hasn't the water evaporated? Isn't Mars almost a vacuum? Why didn't the water evaporate from the soil after being dug up but before being put in the oven?"
Air pressure is very low, though not close to vacuum. The water detected is probably bound in various chemical bonds, and is not ice, which indeed would sublimate quickly if exposed.
"Could there be large underground frozen aquifers?"
These are indeed conjectured. Large parts of Mars could be water glacier with a thin coating of dust.
There is no water per say. It's just that the soil chemical composition is so that if you heat it a "few hundred degrees" a chemical reaction will produce water.
How do they know the water is everywhere? How do they know it's not just in the one place they dug and nowhere else?
Why hasn't the water evaporated? Isn't Mars almost a vacuum?
Why didn't the water evaporate from the soil after being dug up but before being put in the oven?
Could there be large underground frozen aquifers?