Learn Hardcore Korean: hyudaeponi uija araee tteoreojyeosseoyo.

이/가 marks the grammatical subject of the sentence. Here, 휴대폰이 means the phone is the thing that fell.
If you used 은/는 instead (휴대폰은), it would sound more like you’re setting a topic/contrast: As for the phone, it fell under the chair (not somewhere else).

Why is it 의자 아래에 and not 의자 아래에서?

With movement verbs like 떨어지다 (to fall), Korean commonly uses 에 to mark the destination/resulting location: it ended up at/in/under that place.
에서 usually marks where an action takes place or the starting point, so 의자 아래에서 떨어졌어요 can sound like it fell while being under the chair, which is odd in most contexts.

What’s the difference between 아래 and 밑 here?

Both can mean under/below.

의자 아래(에) is very common and neutral for “under the chair.”
의자 밑(에) is also very common and often feels a bit more like “underneath the bottom of it.”
In most everyday situations, they’re interchangeable.

Why is there an 에 after 아래? What is 아래에 grammatically?