I could have bet money that yes and no would be somewhat similar to sí and no... I guess that's another reminder that Vulgar Latin is the real ancestor of all Romance languages.
Ita doesn't really mean 'yes', the true meaning is closer to 'so/thus'. It's used as 'yes' by an implied 'est'.
French 'oui' comes from 'hoc ille', which basically means 'this' (think of how people on the Internet write '^ this' to express agreement).
Overall more common sí (also used in French) comes from Latin sic, which you see in English often after mistakes in an original text as a 'just like that/just so'. It had the same meaning in Latin, moving to just 'yes' in Medieval Latin.
By the way, the usual way you see on the Internet as 'the way the Latins said yes' is 'ita vera', 'the truth (is) thus'
Both Polish and Ukrainian use 'tak/ так' as yes. This is a cognate of Latin 'ita'.
Very interesting, I already noticed some other, quite peculiar Slavic connections... like 'Quomodo te habes' being a word-for-word equivalent of 'Jak się masz' for 'How are you'. To my knowledge, no modern Romance language uses this particular structure, literally 'how do you have yourself'.
What is your source for the cognate? Wiktionary and Vasmer's dictionary only list similar Baltic words as cognates.
Both the Vulgate nae and Greek ναί derive from the enclitic particle -ne, meaning "no/not." Logeion indicates "nae" is used fewer than 50 times; thus I think it unlikely that it is "a usual form of yes."
I remember when I took Latin in high school, we used "Sique" (pronounced like "Seek") as "Yes". This is the first time I've ever encountered "Ita".