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Let her eat when she wants to, no need to take her out of the nest. 45 minutes will not be a problem to the eggs. You will likely not see her eat/drink as it is their tendency to sneak it to protect the eggs.
Blue Barnevelders - yes, I have some. No, they cannot be sexed as day olds. Blue will not show up until they feather in their wings. By 4 weeks you should be able to tell the sex.
I don't like to give my hens more than 12. It's a lot for them to sit on and they have to have room for their legs too. The eggs just end up getting broken. My huge Barred Rock I gave 12 eggs, and 3 got broken in the nest. She has 9 left to hatch this week.