mauseuga chaeksang araee tteoreojyeosseoyo.

Because 떨어지다 means to fall and is an intransitive verb.

• 마우스가 = the mouse is the thing that fell, so it is the subject
• 마우스를 would mark mouse as a direct object, but 떨어지다 does not take a direct object

So:

• 마우스가 떨어졌어요 = The mouse fell
• If you wanted someone dropped the mouse, you would use the transitive verb 떨어뜨리다, as in 마우스를 떨어뜨렸어요

책상 아래에 means under the desk.

Breakdown:

• 책상 = desk
• 아래 = below, under
• 에 = location/destination particle

So 책상 아래에 literally means at the area below the desk.

In Korean, location expressions are often built like this:

• 책상 위에 = on the desk
• 책상 옆에 = next to the desk
• 책상 앞에 = in front of the desk
• 책상 아래에 = under the desk

The 에 marks the place related to the action.

With 떨어지다, 에 often shows the place something ends up or falls to.

So in this sentence:

• 책상 아래에 떨어졌어요 = fell to/ended up under the desk

Without going too technical, 에 here helps show where the falling happened / where the object ended up.

It comes from the dictionary form 떨어지다.

Step by step:

• 떨어지다 = to fall
• verb stem: 떨어지-
• past tense: 떨어졌-
• polite ending: -어요
• together: 떨어졌어요

So 떨어졌어요 means fell in polite speech.

A useful comparison:

• 떨어져요 = falls / is falling
• 떨어졌어요 = fell

This is a very common question.

• 떨어지다 = to fall
  
  • something falls by itself
• 떨어뜨리다 = to drop
  
  • someone causes something to fall

Examples:

• 마우스가 떨어졌어요 = The mouse fell
• 제가 마우스를 떨어뜨렸어요 = I dropped the mouse

So this sentence focuses on what happened to the mouse, not on who caused it.

In modern Korean, 마우스 usually means a computer mouse.

For the animal, Korean usually says 쥐.

So in most everyday situations:

• 마우스 = computer mouse
• 쥐 = mouse/rat as an animal

That said, context always matters. In this sentence, 마우스가 책상 아래에 떨어졌어요 strongly sounds like a computer mouse fell under the desk.

-어요 makes the sentence polite and natural for everyday conversation.

So 떨어졌어요 is a standard polite form. It is appropriate in many situations, such as:

• talking to someone you do not know well
• talking to a coworker
• speaking politely in general

Other possible styles:

• 떨어졌다 = plain style
• 떨어졌어 = casual/informal
• 떨어졌습니다 = formal polite

So this sentence is in a very common, useful level of politeness.

Yes, you could, but the nuance changes.

• 마우스가 focuses on the mouse as the subject of the event
• 마우스는 makes the mouse the topic, often with a sense like as for the mouse...

Compare:

• 마우스가 책상 아래에 떨어졌어요
  
  • neutral description of what happened
• 마우스는 책상 아래에 떨어졌어요
  
  • may sound like you are talking specifically about the mouse, possibly in contrast to something else

For example:

• 키보드는 책상 위에 있고, 마우스는 책상 아래에 떨어졌어요
  = The keyboard is on the desk, and the mouse fell under the desk

So 가 is the most natural default choice here.

Korean word order is more flexible than English word order.

The original sentence:

• 마우스가 책상 아래에 떨어졌어요

You could also say:

• 책상 아래에 마우스가 떨어졌어요

Both are natural. The difference is mostly about emphasis:

• starting with 마우스가 highlights what fell
• starting with 책상 아래에 highlights where it fell

The verb usually stays at the end in Korean.

Yes. 책상 밑에 is very natural and common.

Both mean under the desk:

• 책상 아래에
• 책상 밑에

A rough nuance:

• 아래 can sound a little more general or neutral as below/under
• 밑 often feels more like the physical space directly underneath something

In this sentence, both are fine:

• 마우스가 책상 아래에 떨어졌어요
• 마우스가 책상 밑에 떨어졌어요

Because 책상 아래 works as one location phrase: the area under the desk.

Structure:

• 책상 modifies 아래
• 아래에 marks the whole location

So the logic is:

• desk + under + at/in

Not:

• desk-at under

This pattern is very common in Korean:

• 집 앞에 = in front of the house
• 학교 뒤에 = behind the school
• 의자 옆에 = next to the chair
• 책상 아래에 = under the desk

So 책상 아래에 is the normal structure.