Raising and Breeding Finches?

I just got 2 finches from Petsmart. One is a solid white zebra finch and the other one is a classic zebra male. Now I know that with females they have a lighter colored beak so I'm pretty sure it's a female, but they haven't touched their nest or the stuff to make a nest that I put in their cage. They sit on the nest and sleep.

I noticed when I got the white one from the store the back of her neck was missing a few feathers and you could tell right where her beak is there is a tiny hole. I don't know where that's from, but they will be sitting on the nest and he will start grooming her at the back of the head and neck. I noticed he had plucked out a feather. She would just sit there then get a little agitated. Is he being mean? That's the only time they get a little irritated with each other. Will they breed?

Also I noticed when I was choosing my birds at the pet store that they pant with their beaks open. The first set of birds I had a few years ago didn't do that, but these 2 do. Also the male will sorta pant and squeak. Is he sick? I have only had them 2 days. I'm starting to think Petsmart needs to take better care of their animals.

By Sierra S