I would also say there is no such a word in Russian like "простойный" if I had not read this topic

As to "простой", yes, we have two different words of different structure. That is a pure coincidence.

"простой" (simple): "прост-" is the root, and "-ой" is the adjective ending (nominative masculine singular), the ending is stressed. When declining this adjective, we have:
простой - простого - простому - простым - простом (masc); простая - простую - простой - простой - простой (простою) - простой (fem); простое (neut); простые - простых - простым - простыми - простых (pl).

"простой" (idle time, standing idle): "про-" is a prefix which expresses duration here, and "-стой-" is the root (as Anixx noted, it's of the same origin as English "stay"). Since this word is a masculine noun, it has the zero ending in Nominative Singular. When declinining this noun, we have:
простой - простоя - простою - простоем - простое (sing); простои - простоев - простоям - простоями - простоях (pl).

So, there are three coinciding forms:
простой: adjective (Nom.Masc. or Gen.Fem. or Dat.Fem. or Instr.Fem. or Prep.Fem) vs простой: noun (Nom.Sg);
простое: adjective (Nom.Neut) vs простое: noun (Prep.Sg);
простою: adjective (Instr.Fem), it's an alternative version of "простой" form; vs простою: noun (Dat.Sg).

Any other form is unambiguous, e.g.: простые - only adjective (Nom.Pl), or простоем - only noun (Instr.Sg) etc.