As for wiping over the khimar, we say the khimar in this case has different situations: either it covers the hair completely and nothing of it appears.
So we say it is better for the woman to remove the khimar and then wipe over her hair. But if the khimar is transparent and shows some of the hair and.
Or strands of hair, or maybe something appears from the front, we say there is no problem for the woman to wipe in that case, and this has been reported from some of the Mothers of the Believers.