Χαίρετε!
If I want to write “No” or write “Yes,” would I use Οὐ(κ) or use Ναί?
Ναι for yes, like in modern Greek, ου δητα, ηκιστα, μα Δι’ου for no.
You will find a lot of relevant options for each in Plato. Do note that if you are looking for variety, and even if not (just to check you understand them), you should think about the constructions of each you intend to use (for instance absolute “ἔγωγε” may be translated often as “yes” but it makes sense that it is restricted in context of appearance).
Note: not convinced the ου can go without complement in “μα Δι’ου”.
Frequently, to answer a yes/no question in the affirmative, the verb is repeated (“did he?” “he did”) or as Callisper noted, a “did/do you/were you/are you” type of question is answered by ἔγωγε. Depending on the question, other formulas may be used. In my experience, ναι is not as common in ancient Greek as “yes” is in modern English. Latin is similar to ancient Greek in this regard.
I’m not sure about frequencies but Plato has “ναί” rather often, to the extent I think it’s not a bad approximation for English response “yes”. Certainly it should be viewed as an unobjectionable option for a student wishing to express “yes” in Greek. I wouldn’t compare it to Latin where ita (esp. unaccompanied by anything) is genuinely rare for “yes.”
Whether there is a reason besides desire for variety why Plato uses such a wide variety of response formulae (for both affirmation & dissent), or what conditions the choice between them (besides obvious cases like “ἔγωγε”), is something I am not sure about. I would invite references to scholarship on this. In any case I’ll go ahead and claim that there is no single affirmative response formula as common as “ναί” in Plato (see also Edit).
I think that the strategy of repeating the questioner’s verb, while not infrequent in Greek, is the main way of handling things in Latin (the use of an alternative, like “ita est”, being marked); whereas in Greek it is less frequent than some other formulae (e.g. “ναί”, “πάνυ μὲν οὖν”, “παντάπασί γε”, “ἀληθῆ λέγεις” - please note: choice of a few examples based on my own experience with Plato, and does not have scholarly credibility, nor am I saying these are all the most common though I do think they’re up there).
TLDR - you can say “yes” in Greek. You can’t in Latin.
Edit: checking TLG, ναί is used 827 times in Plato. That’s a lot, I’d say. Comparing to this frequency for “yes” in American English - https://www.wordfrequency.info/free.asp?s=y - “ναί” (alone) is about 3.3x as common in Plato as “yes” in American English, in fact. Even “πάνυ μὲν οὖν” is 1.35x as common as our “yes”. (Of course remember Plato is writing dialogues, which is presumably why the rate seems so much higher - one imagines affirmative response formulae of this kind are about as common in Greek as in English)