Converting closed tread stairs to open tread stairs
A stringer is what supports the treads of a staircase from below. The treads sit on the stringers. There are likely three - one at each end and one down the center, continuous up any single run of steps. The walls that skirt your steps on the outside and hide the step’s edges are merely decorative and can be removed or modified without affecting the structural integrity of the staircase.

Take down the walls you need to, to uncover the ends of the steps, then reframe the walls so the framing is flush with the outside face of the outside stair stringer. Then finish with new drywall, wood, whatever you fancy. 

The staircase you have with the switchback in it with the wall in the middle - that decorative wall in the middle can be taken down to the level of the middle landing and made flush with the floor there, creating a little shelf.