Well, I don't know anything about Zebra Finches specifically, but I do know a few things about birds (do an online search on Zebra Finches to find out specifics). The mother birds usually feeds the babies, you don't worry about that.
The daddy bird usually stays out of it, but not always, so find that out. Some daddy birds kill the babies, also find that out, you may need to separate mother and babies from him until they are quite a bit larger. In fact this information pretty well covers the whole spectrum of "nature". Hope this helps, kinda :).
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