"So why does Nova need a gun?"
same reason why any ghost needs a gun.
Nova is the most powerful psychic in the SC Universe, aside from Kerrigan. She's a 10 on the Psi scale, the next strongest being Tosh (Post Spectre) at 8. She can level ten city blocks of area with about three minutes of concentrated thought.
For reference, Kerrigan is the reason the scale goes past 10. They tested her, she was literally off the charts, so they extended them (I'm not sure /what/ she's at. They listed Abberation as Class 8 Psionic, and Kerrigan as 13, but Abberation never does anything. Maybe that scale is logarithmic, while the normal Psi scale is linear).
For more reference: 6 on the scale is telepathic, 8 is telekinetic.
On topic, though, it's because no matter how psychically powerful you are, having a gun is always a plus. It just means more options. And all Ghosts are trained as soldiers, because not all ghosts are crazy like Nova, so she got the same basic training and decided to stick with it, I'd guess.
Sorry, a bit off topic here. Was Kerrigan rated 13 pre or post infection? If post, was that changed with the destruction of her inhibitor in the SC1 mission? If pre, where does she rate now? If you know that is, not too familiar with stuff outside the games. =/