науки с маленькой буквы предметы в школе (в расписании) с большой

Not really, unless they are being used as course titles or are names of languages which would normally be capitalised. See https://www.umgc.edu/current-students/learning-resources/writing-center/writing-resources/grammar-help/capitalization.cfm https://capitalizemytitle.com/ufaqs/do-you-capitalize-school-subjects/

Yes, they're always capitalized.