+ㄹ/을 까요? means "shall we?" 학교에 갈까요? - Shall we go to school? 지금 잘까요? - Shall we sleep now? 내일 공부할까요? - Shall we study tomorrow? So if you listen/read some kind of 까요?, then that means "Shall we?". I hope my explanation will be helpful to you :)

까요? has many meanings. 지금 학교에 갈까요? can mean "Should I go to school now?" or "Do you want me to go to school now?" But since the omission of the subject is common in Korean, 지금 학교에 갈까요? can also mean "Shall we go to school now?" The best way is to memorize a couple of example sentences. They won't cover every usage but that's pretty much all you can digest at first.

Hi, Danielle :) Should I go to school now? should be '지금 학교에 가야 해요?' 지금 학교에 갈까요? Shall I(we) go to school now? should, must=해야하다, 해야한다

While one of the two main usages/meanings of (으)ㄹ까요 is "Shall I/we V", we don't really say "shall" much in modern American English last time I checked ㅎㅎ So I would say that "Should I go to school?" and "Shall I go to school?" have the same meaning. Of course, "Should I go to school?" could also have the meaning of "Do I have to go to school?" In English, we use various words to convey our meaning. In Korean, we use grammar to convey nuances in meaning. So it depends on what you meant by "Should I". That is how you to determine which grammar point to use.