Hazlebee is right about 예 being slightly more formal than 네, (which is why 네 is used more--예 is pretty much for talking to superiors in the workplace, or to show great respect to elders or persons perceived to be "important". But Cely makes an excellent point about the fact that all affirmative responses, 네, 예, 응, are an agreement to the question as it has been asked, and can lead to great misunderstandings by those not familiar with that aspect of the language. When the negative question "Don't you like the food?" is put to you, the polite response is "No, it's good." If You say, "Yes, I like it." The first thing to hit your host's ear is the "Yes" which signals agreement to not liking the food. I have yet to read all of the notes, so I don't know if this is covered in the course. As it is still in Beta, that would be a good suggestion.
Aside from 예 being just the sound, it is informal while 네 is the formal way to say yes and you will hear it more often. Something that i dont like about this app is that it doesnt explain that the korean yes(네) is not like the english yes (idk if it will explain it later). The korean yes (네) agrees with what the person you are talking with is saying. The same thing applies to the korean no (아니요 formal 아니 informal). When you say 아니요 you are disagreeing with them. For example if someone asks you "you dont like apples?" You say 네 to agree with what they are saying meaning you DONT like apples and 아니요/아니 to disagree if you DO like apples.
I think depends on specific situations. If I'm talking to my friends and somebody asks about apples it's natural to reply the way you said. But if someone asks "Do you mind if I sit here?" I tend to instinctively reply "Oh yeah of course" as in "Yeah of course you can sit here", which leads to endless confusion because people take it as "Yeah of course I do mind"...
The response given depends on a lot of things and can be colloquialized or not. I don't colloquialize my answers and would answer like you: "No. I don't 'don't like apples' (I do like apples)"
Many people, however, won't say "no", since that creates a double negative that has to be resolved, and will therefore colloquialize a "yes" to mean "yes I do".
It gets worse when you have double negatives in the question, causing triple negatives in the answer. Or the phrase "is it not..." causing colloquializations. "Is it not cold?" "No, its not cold (colloquialized to say its warm)" vs "No, its not 'not cold' (literal to say its cold)". Languages can be dumb...
It is like the Rwandese word "oya", sounding like "Oh, yah" meaning "no". ;) Or the Saxon (Germany) word "no" or "nu" meaning yes. ;) It is worth watching Korean movies/soaps a lot just to get used to it (and all the other words, too), even if you hardly understand anything at the beginning.
There are so many ways to say yes in Korean, it can get a bit confusing. 네 is probably the most used way of saying yes. I believe that 네 is a less formal way of saying yes than 예. 예 Is also quite common to hear. It's more formal than 네, but too formal to the point where it would be weird to say to a friend. 네 and 예 are basically interchangeable despite one being more formal than the other. 응 is super casual, but also means yes. But you might want to be more careful as to when you use 응.
Hearing "Dae" when they say "네" is probably because ㄴ and ㄷ are both pronounced in Korean with the tongue tip touching the back of the front two top teeth. So, they could sound similar depending on emphasis by the speaker.
Ye is a different word (예) with the same meaning.
For Koreans, both "ㄴ" (N) and "ㄷ" (D) are sounded out with the tongue touching the front two teeth. So, it's common for them to sound really similar, especially when it's the first part of a syllable.
In contrast, in English, we sound out "N" with the tongue touching the roof of the mouth in the middle-to-rear and with "D" the tongue touches the roof near the teeth.
What you're hearing as "데" is, in fact, "네".
In English, when you make the "n" sound, your tongue touches the roof of your mouth directly behind your front two teeth. And when you make a "d" sound, your tongue touches the roof further back.
But Koreans say "ㄴ" (n) and "ㄷ" (d) with their tongue in the middle of the front teeth. So, often they'll sound nearly the same.
And the difference between 네/예 vs 응 is that 응 is informal. You use it with people you're close to or maybe someone "below" you in the social hierarchy.
Because it may not be someone implying an answer before they have one, they may be asking a neutral question.. 'you don't like apples?' versus 'Do you not like apples?'.. The second one they have not implied you don't and are just asking, so it would come across rude to assume they are by using right or wrong, it would make more sense to say yes or no, and then say what you really prefer to communicate clearly, such as 'yes I do not like apples', or 'no, I do like apples'. And, yes or no, can mean agreement, depending on the context. Such as when someone is wanting you to confirm something they are asking or not, such as with the implied question 'you don't like apples'.