Space is cold, it can easily be -170 C° Your cheese will not be spoiled for a hell of a long time. Cold boiling is because of a low pressure, however, we're in a celestial body, it has a lower gravitational force, but still. Also, that water isn't alone, it's bound to various other materials too. Water-containing life can and will survive in space without any special equipment, and cheese isn't even alive in the first place.
Cosmic radiation is a factor, but I don't think it can get through the rock easily.
So yes, You can has a cheezburger.
The second part is an obvious No, We can only assume, and a yes, we can easily be almost sure, that cheese hasn't got spoiled (entirely).
Friendly note: For cold boiling, we need the stuff to have energy, so it would wiggle around enough, low pressure will lower the energy wiggling needed to break free, however in cheese and ice, there's a stronger connection between the atoms, thus will boil if they're given more energy and not just low pressure.
Watch, what happens to vacuumed flesh:
Spoiler: Absolutely nothing. :)
Hope you enjoyed this little answer.