I have some infertile eggs in my finches sleeping/nesting box.She has had nothing to do with them.?

For over a year she has used it as her sleeping nest.I put our male Canary into share the cage, soon after the eggs appeared,but i have been told that a Male Canary and a Female Zebra Finch would not mate and that the female Finch can lay eggs without a male bird?Is this correct and if so, should i keep them together?I have not seen them mating but they seem to get on ok together sharing the cage.What should i do with the eggs?