Shokudaikiri would definitely believe and if his other Date-gumi didn't he would write notes to santa apologizing and being like "Please forgive them they are so sweet and kind, they mean well!" and make many snacks for Santa.
Kara probably believed in Santa since, according to Canon, she came to Earth right around the holidays. she was young enough to be convinced to believe in him despite Kryptonian logic telling her no XD