byeoge georeo dun sajini tteoreojyeosseoyo.

It comes from:

• 걸다 = to hang something
• -어 두다 = to do something and leave it in that state

So 걸어 두다 means to hang something up and leave it there.

In 벽에 걸어 둔 사진, it describes a photo that someone had hung on the wall and left there. It sounds a bit more deliberate than just saying the photo was hanging.

Because Korean relative clauses come before the noun they describe.

So:

• 벽에 걸어 둔 사진 = the photo that was hung on the wall
• literally, [on the wall hung-and-left] photo

Korean does not need a word like that or which here. The whole verb phrase directly modifies 사진.

-어 두다 adds the idea of:

• doing something in advance
• leaving the result in place
• keeping something in that condition

So 걸어 두다 is not just to hang, but to hang up and leave hanging.

That is why it fits well here: the photo had already been put on the wall before it fell.

Because 둔 is the form used when the verb phrase modifies a noun and refers to a completed action.

• 걸어 둔 사진 = the photo that was hung up
• 두다 is the dictionary form, so it cannot directly modify 사진
• 두는 would usually sound more like a habitual or ongoing action, which does not fit as well here

So 둔 is the natural modifier form in this sentence.

It is based on 걸다.

• 걸다 = to hang something
• 걸리다 = to be hung / to get caught

Here, the sentence suggests that someone hung the photo, so the transitive verb 걸다 is the source.

Compare:

• 벽에 걸린 사진 = the photo that is hanging on the wall
• 벽에 걸어 둔 사진 = the photo that someone hung on the wall and left there

The second one emphasizes the earlier action more clearly.

Because 에 is used with 걸다 to show the place where something is attached or placed.

• 벽에 걸다 = to hang on the wall

By contrast, 에서 is more often used for:

• the place where an action happens
• the place something starts from

So with 걸다, 벽에 is the normal choice.

If you wanted to say explicitly it fell from the wall, then 벽에서 떨어졌어요 could be used. But in this sentence, the wall is already mentioned in the phrase describing the photo.

Because 사진 is the subject of the main verb 떨어졌어요.

The full subject is:

• 벽에 걸어 둔 사진이 = the photo that had been hung on the wall

So 이 marks that whole noun phrase as the subject of fell.

Yes. Korean often leaves out the doer when it is clear from context or not important.

So 벽에 걸어 둔 사진 could mean:

• the photo I hung on the wall
• the photo we hung on the wall
• the photo someone hung on the wall

Korean does not need to state that person unless it matters.

In this context, it naturally means fell or fell off.

떨어지다 is used for:

• something falling down
• something becoming detached and coming off

Since the photo was hanging on the wall, English often translates this as:

• The photo fell
• The photo fell off the wall

Both capture the idea well.

Yes, that is also natural.

Both -어 두다 and -어 놓다 can describe putting something into a state and leaving it that way.

Very roughly:

• 걸어 둔 = hung it and left it there, with some sense of prior arrangement
• 걸어 놓은 = hung it up and it is set there

In everyday speech, the difference is often small, and both versions sound normal.

Because 두다 is functioning as an auxiliary verb here, and in standard spacing it is usually written separately:

• 걸어 둔

In casual writing, you may also see:

• 걸어둔

But the spaced form is standard and very common in careful writing.