Regarding Pan, she is the daughter of a half-Saiyan and a pure human, so she is a quarter Saiyan, however Gohan, her father, is also only part Saiyan but the first half of DBZ frequently hinted at how powerful Gohan is.

Anyway, their powers don't come from their heritage. They come from control of their spiritual energy, derived from Chinese and other Asian mythology what with Qigong and all that. The Saiyans are just particularly powerful naturally, but with training and focus anyone can use his spirit (a theme the plot seems to have forgotten loooong ago).

That said, yeah, don't kill Pan. If anyone, pick on one of the more mature pretty women in Dragonball, like Android 18, 18 year-old Chi Chi (from the end of Dragonball), or young-adult Bulma, as she appeared in Dragonball initially at 16 and latterly at 22 years of age.