"I do not have to say anything."
Translation:Nie muszę nic mówić.
In positive sentences you can In negative it changes and nie muszę=I don't have to; nie mam (czegoś robić)= I shouldn't do this, I'm not supposed to do it to a bit like doesn't have to <> must not
mam wrócić do domu o ósmej = I have to come back home at eight nie mam wrócić do domu o ósmej- (weird) Nie mam wracać do domu przed ósmą= I shouldn't come home before eight ( my roomate has a boy around ) Nie mam wracać do domu po ósmej = I shouldn't come home after eight (either I have to come before eight or altenatively, if it's after eight I'm not supposed to go home )
No, and no. "I don't have to say anything" means "I am not obliged to say anything" or we could even interpret it as "I have the right to remain silent" ;)
"I have no words" translates quite literally as "Nie mam słów", but more often idiomatically as "Brak mi słów".
"Nie mam nic mówić" - that kinda makes sense, because "mieć" can be a modal verb which is similar in meaning to "to be supposed to", so "Nie mam nic mówić" could translate to "I am not supposed to say anything". But that sentence seems ambiguous, it could be used for example if you're in a play at school but your part is not a speaking part, you just stand there. "Mam nic nie mówić", on the other hand, it's "I am supposed to say nothing", "I should stay silent".