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Best thing to do with any eggs you're uncertain of is to crack them into a small cup and look/smell for anything off. If it looks normal, you're good to add them into a batter, scramble, or straight to a pan, etc.

Floating only gives you an idea of how old the egg is - since you know these are recently laid, no need to float test.

Should be fine to eat, as long as the "patch" at the end is solid and not cracked through. Maybe the shell cracked as it was being formed and then was repaired before being laid, or it could be just some excess calcium padding on the end there.