Can i keep a female regular finch && a male zebra finch together?

I have a few questions as to whether or not i can keep them together. Because My male zebra finch wont stop picking at my female finch. && its getting bad because she has a lot of bald spots and i think he bit off her toe? So i seperated them the first time, && then put them back but he still wont stop. So i seperated them again. Should i keep them that way? Will her feathers grow back? Also. They lay eggs that never hatch, && the male is always the one to sit on the egg? Is he picking at her because she cant produce a baby finch?