How do I safely paint the walls and ceiling in this high ceiling staircase?
There are three ways:

1) Lean a ladder against the lower wall, put boards connecting it with an upper stair, and put a ladder on top of that.

2) Use a baker scaffold.  Baker scaffolds can be set up with varying height legs. Then put a ladder on the baker scaffold.  This is my recommended solution.

3) Use a 2 wheel edging paint pad that will allow you to cut-in using a pole.
http://www.decoratingdirect.co.uk/viewprod/f/FDDEDGPD/

If you are really careful, this might even look ok.