You could try a breast milk bath if you are able to express. Apparently breast milk has all sorts of healing properties for babies (according to my health visitor anyway) Don't beat yourself up about it though, these things happen x
Bless you! Aloe vera gel. Breast milk bath can be soothing as well (if you have any) or oat bath.
Baby moisturiser will help. Treat it similar to yourself catching the sun. Baby moisturiser will help put moisture back into her legs. I let me little girl be in the sun a little as she gets super cold in the shade and I refuse to put extra layers on her in 30°. I usually let her toes in the sun. She's not yet gone tomato from it but I'm sure it will happen at some point