Railing height and spindle spacing is governed by building codes. Generally, railings are to be 34"-36" high and spindles spaced so that a 4" dia. ball won't fit between them. The depth of the tread will govern whether one needs 1-1/4" or 1-3/4" thick (wide) spindles (so that there's less than 4" between them). Spindles usually come in 36" lengths and cut down (both ends equally) to the size needed to fit between the railing and stair tread.

Thanks acroteria.

Does anyone know what width the spindles in the photos I posted are?

Impossible to tell for sure anybody who answers will be strictly guessing.

No more than 1 1/4 square on a very good guess. Two to a step, spaces between. Fold a sturdy white cardboard to that dimension.....you'll see what I mean. It matters not, stairs and rise and spaces are governed by CODE.