The two go hand in hand don't they? Higher moisture content = more weight, more weight = higher density (provided size is the constant)
Light weight bats with big edges will always be on the dryer/low density side. Particularly given the record pros have with bat care... i.e. very few ever oil bats amongst other things
Yes and no. Willow is a natural product, so some is naturally more/less dense than others.
For example, butterfly willow is known to be heavier than a pure sapwood cleft.
B3 explain it best with their clefts having the density calculated before the bat making process begins. Their clefts are all the same size, and they all have the same moisture content, yet some just weigh more/less as they willow density naturally varies.