How is it that the hints for कल are both "yesterday" and "tomorrow"?
You have to understand it with context. This sentence ends with "आएगा" that is future tense. So "tomorrow" will be used. If instead of it we go for "वह कल आया था" then it'll be for "yesterday", as "आया था" indicates past tense.
So does that mean you can't have simple replies like "And tomorrow?" and must instead say "And what will be tomorrow?" or something of the sort?
And how in the hell does a word like this even come about? This is so curious.
and btw, i noticed you wrote आएगा (just like in the wiktionary table), yet here it's आयेगा (same with "to go"). are both correct?
Is it wrong if I write she will come tomorrow?
Yes, as even with this new ending (येगा/येगी) the final vowel determines the gender of the subject. If it said आयेगी it would be she
Its is a very helpful app