"I do not want to talk with him."
Translation:Nie chcę z nim rozmawiać.
As a native speaker of Polish, I would say that both are correct, but have a bit different meaning.
- Nie chcę z nim rozmawiać - I do not want to talk with him (at this moment).
- Nie chcę z nim mówić - I do not want to talk with him (never ever).
I cannot say if these niuances could also exist in an English phrase.
Actually, Polish Wiktionary puts "rozmawiać" as one of the meanings of the word "mówić", with the example: "Chciałbym mówić z prezesem." Słownik Języka Polskiego - doesn't. It does not seem to me that it is used often in such a way, and "Nie chcę z nim mówić" seems quite weird to my ear, even if it's not technically incorrect.
It's correct and should be accepted. It sounds more formal to me, though. It also has a more narrow meaning. Pehaps, in terms of usage, you can compare it with English speak with sb. In most cases, better use rozmawiać.
Actually, that is the reason I thought it should be correct, because in my native language, namely Croatian, which is a close relative to Polish, there is the same dichotomy between "govoriti" - to speak, and "razgovarati" - to talk (to sb), and we can also say "govoriti s nekim" - to speak with sb, which sounds quite formal.
"jego" doesn't suit this sentence at all. It is either Genitive or Accusative.
"nim" is either Instrumental or Locative, and as this is "with him", that's Instrumental.