Okay, I have owned my zebra finches for several years. The female finch, had a clutch of eggs

. She has for the past few years been living in a large cage, with her son

. I bought them food dishes in the shape of oranges, that were too small to breed in to prevent them from having eggs. Turns out that they were not actually too small

, and mom zebra finch is brooding a clutch of eggs. The only other finch in the cage is her son

, and he has been offering her bedding material. The mama finch has only left the next on rare occasions to get food, and seems to be spending all her time there. But the father zebra finch has yet to sit on the eggs. He does seem interested.
The mother and son zebra finch have lived together for quite some time, and she has in the past always laid dud eggs, but she's never brooded them either.
These are my two starter questions;
First : Do my finches actually have fertile eggs?
Second : How bad would the inbreeding be?