It doesn't. "Ita." means "so.". It should be "ita est.", "So it is." for "Yes." but any conjugated form of "esse.", "to be.", can be left out in Latin.
Correct. It appears this is not strictly Classical Latin. (Or I missed something in Latin class.)
"Ita" is a particle with an affirmative sense to it, but it isnʻt exactly a word you should consider as a generic ʻyesʻ. Think of it something like "It is so" or "That is true." To be more emphatic you can use "Ita vērō!" (long vowel markings included). Compare this to "minimē", which can mean no but is often more precisely rendered as "not at all".
In any case where youʻre not providing those sorts of emphatic affirmatives or negatives, a common tendency is to just repeat the important parts of a y/n question with any appropriate particles - e.g.: "Vidēsne hunc canem?" (ʻDo you see this dog?ʻ) -> "Nōn [eum] videō." (ʻI do not see [it]ʻ)
Will "Yes, I'm feeling fine" be added as a possible answer? Or is it wrong?