why is the transmission and input side of the transfer be spinning more than twice as fast?

The transfer case does nothing to affect these. The only thing it does is cause the output side of the transfer to either spin 1:1 when in Hi range or 4:1 (in my case) when in Lo range. The speed of the input side is controlled by engine rpm and transmission gear selection.
My transfer has a slight whine at any speed. I think this is quite common.