Eggs are generally OK if they don't float. A little tip-up on one end is fine. Full-on bobbing suspended in the water is no go. Also, if in doubt and still wanting to use eggs, crack each one by itself into a bowl, inspect, and put into a group container once it's "approved" for use. You will definitely see/smell the offness of eggs.

Freezers generally do ok in power outages as long as the door stays shut. If you checked the freezer right when the power came back on and stuff was still frozen solid, you're good. Freeze-thaw-freeze does tend to adversely affect food quality, though, so if stuff thawed out mostly or all the way, but was STILL COLD, you can probably triage-eat your way through a lot of it.