As for wiping over the socks:
https://www.assimalhakeem.net/how-to-wipe-over-the-slippers-or-socks/

and wiping over the hijab, Please also watch this video: https://www.youtube.com/watch?v=-uo2_GeWXvI

I started teaching in s school recently.. and I prefer praying Luhr in school. I have heard that brushing off water over the sock is permissable. But I want to know if we should take off the scarf to brush off water over the head? (School hours 7.20 am to 1.30 pm) I reach home by 2.30-2.40