What an interesting structure.
In answer to your first question - Following the Hartley Colliery disaster of January 1862 (see Wikipedia) legislation ensured that all colliery workings had two means of egress. The aim was to ensure that fresh air went down one shaft, was circulated through the workings, and then exhausted up the other shaft (these are generally known as the downcast and the upcast shafts).
Looking at your ground plan it would seem that what you have here is a winding engine house. For this to be true the shaft would have to be in line with the winding drum.
We have excavated several engine houses here in the Peak District and the structure of winding engines is a far lesser known topic than the structure of beam pumping engines. At one of our sites we had a winding engine installed second hand around 1845 and we came to the conclusion that the winding drum was horizontal (which is something we have never seen illustrated).
The engine house probably did not contain a beam pumping engine because a) you do not have a heavy duty bob wall to balance the beam on and b) you would need a shaft equidistant from the cylinder to the bob-wall and from the bob-wall to the shaft in order to operate the pumps.
What I see from your photograph is a winding engine house. To the left is the boiler (which may be an egg-ended boiler) with a stoke hole at the lower end and a chimney base to the top. In the right hand side I would presume the winding engine would stand. However, I would expect it to be sat on plinths to support the engine, flywheel, and possibly, drum. The black marks on the floor are, to me, indicative, of grease spills from greasing the engine.
All this is based upon one photograph, so I might well be incorrect.
Cheers, Dave Williams