Why does ώρα change its “spirit” in the plural declension? In singular, dual and major part of the plural (apart from N and V) the spirit is harsh, in N and V is soft. Why?

I think you’re asking about the initial aspiration? That ‘hour’ in Ancient Greek is ὥρα hɔ́ːraː, but its plural nominative is ὦραι ɔ̂ːrai, not ὧραι hɔ̂ːrai?

… It’s not true. The plural of hɔ́ːraː is indeed hɔ̂ːrai. The breathing marks are tiny, and extremely vulnerable to typos; that’s the only explanation I can think of.

Particularly when combined with circumflex.