from what i have researched it seems they are commonly used interchangeably. however, 밑 can be used to describe something that is connected to the object. for example, the underside of a car or the bottom of the sea.
아래 can in turn be used to describe anything positionally beneath another object, touching or not and regardless of how far under.
personally, for this particular sentence i would use 아래, but seeing as they are used interchangeably i think it is fine either way.
i am not a native speaker though! so if this is incorrect please correct me!!
I think it might have to do with the 가 at the end of the first word. 가 is a subject marker, meaning that it emphasises the subject (the mouse). Had it been 쥐는, the focus wouldn't have been on the mouse but on the topic/description instead (because 는 is a topic marker). In that case, the sentence would have translated to "there's a mouse under the chair", because the topic (i.e. the question of what's under the chair) would have been what was emphasised.
I'm just learning Korean too, though, so I can't guarantee that this is correct. :)
No, not exactly. If we change the sentence to '쥐는 의자 밑에 있다' then, yes, the focus is more on mouse, but this is probably because the mouse is already the topic of conversation. Like, if you saw the mouse, then lost it and someone screamed:
Where is the mouse?! I don't see it! 쥐 어딘데! 안 보여! It's under the chair! 쥐는 이제 의자 밑이야!
This would make more sense. I actually think the OP's sentence should also be an accepted answer.
Actually, my theory is when the noun we're talking about(subject) is after the [noun+preposition],it means, "There is (subject noun)..."
But if the subject noun is before the [noun+preposition],that means, "The (subject noun) is...".
E.g: 집 밖에 나무가 있어요. -Lit meaning- Outside the house,there is a tree. Also meaning, "There is a tree outside the house."
나무는 집 밖에 있어요- Lit. Meaning- The tree(you're talking about), it's outside the house. Also meaning, "The tree is outside the house."