If they are still gathering sunlight and carbon the same way but gaining size quicker then there is just less carbon per cubic cm. There'll be some advantage in being able to get at more light and carbon sooner, but as carbon stored per square meter of land it's probably less.
That is not to say that you could not in principle make trees better, but I think the changes would have to be something fundamental to the cell physiology. A C4 carbon fixation pine tree might be better but it might be easier to turn bamboo into a pine tree than it would be to make a pine tree work with C4. Evolution is really good at balance, tweaking a bit can knock a lot off balance. It's not an impossible feat to make something better but it isn't easy.
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).