concrete stairs with side walls
Do the new steps really need to be suspended? It would be far easier having them sit on grade from a logistics standpoint.
As for forming and pouring in one pour, it would obviously be easier if you didn't need the sidewalls, but it can be done either way. You would cut a form for the inside that would be similar to a stair stringer, but set upside down. The form for the exterior of the wall would be far simpler. Keep in mind though that if the finished exposed product is going to be concrete, you'll need to strip all of this out & finish it all before the concrete sets completely. Easier said than done. If you would plaster the walls (like they are existing) and consider settign brick pavers, cut stone, etc.... for cladding on the risers & treads, the concrete pour itself would be easier to complete, although you'd have quite a bit of additional work to finish the steps off.