"We need to talk."
"Porozmawiać" is a perfective verb so it puts accent on the effect of conversation.
"Rozmawiać" is an imperfective verb so if you used it here, it would sound as if the act of talking were more important than the effect itself.
"Mówić" means "to speak, to talk" but not "to converse".
There is also a verb "pomówić" which is a synonym for "porozmawiać".
That's interesting; does "dziękować" take Dative? I'd never thought about it till now...
Duolingo is rather strict about grammar rules. ( I hate the word for that).
Many Poles use potrzebować+verb, but rules say it is not OK. (Half of the resources say it is German influence, other half that English. )
Yes. As immery wrote, many Poles can use a verb, I'm not even sure if I would notice a mistake like that, but the rules state that it's wrong.