Can I hatch the eggs of my chickens if the rooster and hen are different breeds?
There are no problems associated with hatching mixed breed chickens. If you have a rooster in your flock, he will try to breed ALL your hens, nevermind if your rooster and hens are different breeds or even if they are different sizes, bantam and large fowl. It can be very fun to hatch "mixed" eggs, because you never know what you'll get! And actually, Red Stars and Black Stars are both mixed breed chickens, made from a specific cross in order to provide certain desirable qualities. Easter Eggers are mixed breed chickens, too, with no specific breeding standard other than to select for personality, egg color and laying ability. So mixed breed chickens are not even unusual.
Some of my favorite chickens are mixed breeds: I LOVE my Faverolles-Ameraucana crosses--they are extraordinary layers of pretty green eggs--and my Speckled Sussex-Faverolles crosses are quirky and sweet with good laying ability. If you show chickens, mixed breeds cannot be used for show, but some of the prettiest birds I've ever seen are mixed breeds. Plus, because a few generations down the line you may not know exactly what to expect when your little chick pops out of its shell, the beauty of the birds can be wonderfully surprising! In fact, you may be the ONLY person in the world to have a chicken with those particular genes, so each one is precious and unique.