They're more water, less carbon. So, they are less efficient at carbon sequestration in terms of density. And, they are probably easier for microbes to break back down so they hold the carbon for less time.
Here's a layman's article on the "best trees" for carbon sequestration- http://www.slate.com/articles/health_and_science/the_green_l...
Which is basically forever if you throw away the paper instead of recycle it.
The answer is no, paper mills power themself from trimmings from paper making. They use much less than the mass of paper they produce.
Making paper does not take very much energy. The energy used in cutting and preparing wood is not that much when compared to the amount of wood produced.
So yes, turning wood into paper is carbon negative (in a way, technically it's the growing of the tree).