Where you do things

에 from days 15 and 16 marks a point: where something is, or where it is heading. 에서 marks a stage: the place where an activity takes place. Which one you need depends on the verb. 있어요, 가요 and 와요 are about being at a point or moving to it, so they take 에; 마셔요, 일해요 and 공부해요 are activities, so the place where they happen takes 에서. A quick test is to ask 'is something being done there?', and if so, use 에서.

English uses 'at' for both 'I am at school' and 'I study at school', so the difference stays invisible until Korean makes you pick. Think of 에 as a pin on a map and 에서 as a room with something going on inside it. The pin tells you where a thing is or where it is going; the room is where the action is. 에서 also means 'from' with verbs of movement, as in 런던에서 왔어요, 'I came from London', which you will be able to say after day 20.

살다 sits on the line between the two kinds of verb. Living somewhere is partly a state, like being there, which would take 에 as 있어요 does, and partly an ongoing activity, like working there, which would take 에서. Korean accepts both, and in everyday speech you will hear both all the time with no real difference. It is a useful reminder of what lies behind the rule: the particle follows how the speaker pictures the verb, not a list of nouns.