I doubt the staircase is supported off the wall, if that’s the question you are asking. Is it a straight flight? Is there a newel post on the high end?
Yes. Do a dummy run and see where your levels sit. Use sand under the DPM to make up a few mm if necessary. You may not need any or just a smattering by the join.
I'm not sure £100k is all that significant an expenditutre in this day and age, especially when you consider that hundreds of millions can be spaffed in an instant. If a £100k went on to buy me £20 billion in revenue I'd be happy with that.
Firstly, those bricks in the red box have to go.
By the time you have laid a bit of blinding sand, DPM and your insulation, glued floor deck, you will find it will line up perfectly.