Negative questions like this are best avoided by native English speakers because they are so hard to answer ("Yes, he didn't give me advice? No, he did give me advice? Help!!"). I notice that my father, who is a native Hungarian speaker, asks negative questions like this a lot, which makes me suspect that they are quite common in Hungarian. I think they're best translated to English as a regular statement sentence like with a question mark at the end "The boss didn't give you advice?".
Yes, negative questions are very common, and there are typical ways of answering them to avoid the kind of logical confusion that you're talking about. Your advice about rephrasing them positively (or structuring them carefully to make them easy to answer) when translating to English is absolutely right, in my opinion.
One particular thing to be aware of is that a negative question in Hungarian is often a way of being a bit polite, especially when offering things or asking questions-that-could-be-taken-as-suggestions.
In English, "Do you want tea?" is normal and neutral with no expectation about what the answer should be. On the other hand, the negative version, "Don't you want tea?" carries more of a connotation like, "Really? You don't? I expected you would!" or, with a certain tone of voice, even, "Don't you want tea? I kind of think you should!"
But in Hungarian, the negative question Nem kérsz teát? is a totally normal, polite, and neutral way of asking about it without any of those connotations. And you could politely answer either (among other possibilities), Nem, nem kérek ("No, I don't want any") or De, kérek (I do!) In this formula, de is like "On the contrary, I do!" You can pad that out a little to De igen, kérek with the same meaning.
In tone, I suppose it's something like, "Won't you have some tea?"
Very good explanation indeed! Yes, exactly, Hungarian has an easy way of answering negative questions, that is why they can easily be used.
Let's make it very simple. "Igen?" will symbolize a positive question, "Nem?" will symbolize a negative one. Here are the various scenarios:
A: De (igen).
Hungarians might have a little problem grasping the lack of an equivalent of "de" when they are facing a negative question in English.
"Didn't you bring money?"
"Yes (I did)".
Quite weird for the Hungarian ear.
I think German has a word that plays a similar role: "doch". I need confirmation on this.
If you want to "play" "yes-no-yes-no-yes-no.." with your sibling or friend, you can go like this:
Nem - De - Nem - De - Neeeem - De igen! - De neeeem! - De igen! - De mondom, hogy NEM! - De igeeeen! - Neeeeeem! - Deeeeeeeee! - .....