Very interesting… I don’t think you’re in trouble in the third movement; I’d say the F in the chord is correct as marked, as I listened to multiple versions, and none played a G. (BTW, what a lovely movement it is! Prokofiev at his most magical!)
There is, however, great variation in the recordings regarding the second movement spot. Yefim Bronfman is the only one to play as you have written, D-F sharp. A few others play D-F natural, but the great majority play F natural - A, matching the C-E of two bars earlier. The piece’s dedicatee, Sviatoslav Richter, plays D-F natural in his earlier Prague recital, while two later Richter performances have F natural - A. I’m not sure if Prokofiev made any small revisions, but I do know composers in general sometimes fret over deciding such things. I do not know what the best edition is, but if we are without such a thing the most logical answer is to play F-A, matching the pattern of the run two measures prior. It’s the most logical technically, musically, and it sounds the best.
I hope this helps, and I offer you thanks for giving me reason to investigate this sonata again. The third movement truly made my day!
Dave