Why is "Ich habe keine Zeit nun" wrong?
The word order is off.
Ich habe jetzt keine Zeit is the proper way to express this sentence. If you said "Nun, ich habe keine Zeit" you'd be saying "Well, I don't have time".
True. But you can say: Ich habe nun keine Zeit with nun as a synonym of jetzt.
....which I would likely understand as "as a matter of fact". In "Nun habe ich keine Zeit" it conveys more an idea of "now", at least to me....
In spoken language you can hear if it's meant as an actual time statement or as a modal particle.