Dwarves will generally sleep wherever they see fit unless they have an assigned bed, in which case they will prefer this one. Sleeping in an assigned bed does give happy thoughts, being unable to makes a dwarf unhappy.
However, you don't generally have to bother with assigning beds since dwarves will claim unassigned bedrooms for themselves automatically.
Just a side-note: married dwarves and children share beds.
The thing about screwpumps in Dwarf Fortress, is that they can either be automatic (receiving power from a wind/watermill) or dwarf powered. Of these, only the former transfers power, as a dwarf manning a screwpump does not provide power, but rather sidesteps the power requirement entirely.
If however, you were to hook any pump in your pumpstack up to a power source with enough power for the entire stack (100 power in your case), assuming you built the pumpstack correctly, the power in the hooked-up screw pump will transfer to the adjacent screwpumps (and so forth).
Because of this behavior (it's the basis for the Dwarven Water Reactor), any pump with manual power will eject its operator if it gets enough power to operate automatically instead.
Have you seen this .GIF? It shows how to ensure the power transfers properly between levels.
Here's what you have:
If you channel that space and then rebuild the screwpump, power will flow between the connected machines and the screwpump below will no longer need to be manned (dwarfed?)
All screw pumps have two tiles -- one which the dwarves stand on to operate, and one which acts as a wall. This latter part needs to be constructed hanging over an open space to facilitate the transfer of power (as the former part must be constructed on solid ground).
Best Answer
No. A single bed to anchor the room and mark it a Dormitory will assign all beds to that dormitory.
If you assigned a dormitory to each individual bed you'd get a dozen individual overlapping dorms. Probably not what you want as they'd divide the quality value.