Like the others mentioned, bearded dragons rarely eat out of the egg. They are full of yolk from the egg and this lasts for several days to a week. Wait a few days then offer small crickets, a quarter inch or so, or even small phoenix worms (just not the ones that have a dark shell, just the white/clearish ones). Dust as already suggested.
You can put quarter inch crickets into a shallow lid or bowl, to help prevent them from running off. Crickets a quarter inch and smaller are not really good at jumping so they tend to just crawl around. If you are keeping more than one per container, provide either a large feeding dish or better yet several dishes so each dragon has a chance to eat. I also recommend housing no more than 3-6 per container. Separate any that get bigger than the others to prevent it eating all the food and preventing smaller babies from eating/basking.
As for your eggs, unless your incubation rose in temperature, a little cool down due to lack of power won't be a problem, just keep incubating till they either hatch or rot. A good well insulated incubator will not lose heat fast, so the temps may not have dropped too much if the power outage was low. At worse, it would reach room temperature and as long as that wasn't below 60F you shouldn't have any worries.
-----
PHLdyPayne