1_T_Submariner:The Air in your tank and or the tank it self does not significantly expand as you change depth.
The reason can get more air from your tank as it runs low is that the pressure on the out side is reducing as you go up allowing your regulator to have a positive pressure differential which allows air to flow out of you regulator.
I'm not familiar with the internal construction of the J valve. I'm sure someone will answer your question on that.
My understanding of how the "J" valve works is that it mechanicaly prevents the last few hundred lbs of tank air from being released until the operating handle is pulled down by the diver.... thus providing a short (depending on your depth) amount of "reserve" air.