I have some difficulty to understand where to put नहीं in sentences. Is the rule like this: मुझे नाश्ता नहीं पसंद = मुझे नाश्ता पसंद नहीं है ?
What about sentences like "I don't eat breakfast" or "I am not eating breakfast"? How to translate them?
I'm not mother tongue, but I think, for the examples you gave, मुझे नाश्ता पसंद नहीं है would be really stressing the fact that you don't like it (and when saying this the stress would fall on the नहीं). Sort of equivalent to "I do NOT like breakfast". The other form (मुझे नाश्ता नहीं पसंद) is simply a statement "I don't like breakfast."
"I don't eat breakfast" = मैं नाश्ता नहीं खाता/खाती हूँ
"I am not eating breakfast" मैं नाश्ता नहीं खा रहा/रही (optional हूँ)