I confirm. When someone is interested in your purpose rather than your reason, it's often a signal of disapprove) But, not more than in any other language, e. g. "Why" vs "What for"
I like to think of it as a past/future thing, with почему being the past and зачем being the future. What past thing is causing it to be that way, vs. what future thing is it trying to accomplish by doing what it's doing.
In English, "Why is she dating him?" can be negative or not, depending on tone-of-voice. "What is she dating him for?" is negative - it's actually a rhetorical question (a self-answering question, or one which does not require an answer because the answer is obvious) or just a negative statement put in question form.
That depends on what you're trying to say. If what you're looking for is a kind of surprised or disapproving "what's she dating that guy for?", зачем has that connotation.
In some contexts "why does she date him?" might be used, especially when emphasising the word "does". I'm reporting.
In that context, it's still most natural to use present continuous and stress "is" - "why is she dating him?"
It can be translated as "dating" and as "meeting" ( with now romantic context), yes
I am meeting with my friends today. Я встречаюсь с моими друзьями сегодня.
"What is she meeting him for?"? :/ I mean... if they use зачем I am going to translate it into "what [...] for", so I think it's fair if it were accepted.
By the way, why is зачем used here instead of почему?
It may be not a dates but ordinary meetings, like friends or formal relationships. In this case "зачем" is perfectly fit, meaning "for what purpose" (почему will mean "for what reason", "why"). If it's about relationships, all variants are allowed (including "для чего") and all have slightly negative background, like "why she's dating him?"
there is no proper translation of "them" in russian. of course, you can say "с ними", but the person you are talking to will get it as she is dating more than one person
I think it's not wrong, but in English you'd have to use he instead of him (when the person is the subject). Why are she and he dating?
Why do I have to use present continuous tense here? Why is simple present wrong?
"Dating" is only done in continuous tense. I guess because "to be dating" is an ongoing state, rather than a repeated action. If you're referring to the action of going out together, then you can use present simple: "Why does she go on dates with him?"
I disagree. "Why does she date him?" is equivalent to "Why is she dating him?" Both imply on-going action in a kind of present sense, because, in order to "date" someone, you have to go out with that person socially on more than one occasion - more than one date.
That's really what the question asks: "Why does she periodically meet him for social engagements of a more personal nature?" or "Why has she been meeting him for social engagements and why does she continue to do so?"
Certainly, dating someone involves repeated actions, but you don't say "I'm dating her tonight", you say "I'm going on a date with her tonight". I'd argue that "she's dating him" isn't referring so much to the specific action of meeting him for social engagements as to the continuous fact of being in a romantic relationship with him.
Is the grammar the same for "Why is she meeting him?" Would one use a different verb?
In other words, is встречаться c [person] an idiomatic phrase meaning "to date [that person]"
The grammar's the same. "Встречаться с" does not necessarily mean "dating", it depends on context.
"Dating" is out of date. Why is she seeing him?" or better "Why is she going out with him?"