Learn Hardcore German: Ich hänge den Schlüsselbund sofort an den Haken neben der Tür. - I hang the key ring on the hook next to the door immediately.

hängen (transitive) = to hang something (up) / to put something in a hanging position:
Ich hänge den Schlüsselbund an den Haken. (I hang the keyring on the hook.)
hängen (intransitive, state) = to be hanging:
Der Schlüsselbund hängt am Haken. (The keyring is hanging on the hook.)
sich hängen is different and usually means to hang oneself (so you generally do not use mich here).

So in your sentence it’s the normal transitive verb “to hang (something) up.”

Why is it den Schlüsselbund (accusative)? How do I know it’s the direct object?

Because den Schlüsselbund is the thing being acted on—what you’re hanging. With a transitive use of hängen, the object is in the accusative:

Ich hänge den Schlüsselbund ... (accusative masculine: der → den)

A quick test: ask “What am I hanging?” → “the keyring.”

Why does it say an den Haken (accusative) and not an dem Haken (dative)?

With “two-way” prepositions like an, case depends on meaning:

accusative = direction / change of location (“to/onto”)
Ich hänge den Schlüsselbund an den Haken.
dative = location / no movement (“at/on”)
Der Schlüsselbund hängt am Haken. (= an dem Haken)

Here, you’re moving the keyring onto the hook, so an + accusative.

What’s the difference between an and auf here? Could I say auf den Haken?

Typically you say an den Haken because the idea is “hanging from/attached to” something (hook, wall, peg).

an den Haken hängen = standard collocation for hooks
auf tends to mean “on top of a surface.” A hook isn’t really a surface you place something on, so auf den Haken sounds off in most contexts.

Why is it neben der Tür (dative) and not neben die Tür (accusative)?

neben is also a two-way preposition:

dative = position (“next to”)
neben der Tür = next to the door (location)
accusative = movement toward a position (“to next to”)
neben die Tür = to a spot next to the door

In your sentence, neben der Tür describes where the hook is located, not where you’re moving something to next to the door.

What does neben der Tür attach to—Haken or the whole action?

It most naturally describes the hook:

an den Haken neben der Tür = onto the hook that is next to the door

German often stacks noun phrases like that without extra commas or relative clauses. You could also make it explicit:

... an den Haken, der neben der Tür ist.

Why is it der Tür (dative) and not die Tür?

Because neben is taking dative here (location), and Tür is feminine:

nominative: die Tür
dative: der Tür

So: neben der Tür.

Where does sofort usually go in a sentence like this? Could it go later?

sofort is an adverb of time. Common positions:

After the verb (very common): Ich hänge den Schlüsselbund sofort an den Haken ...
Earlier for emphasis: Sofort hänge ich den Schlüsselbund ... (more emphatic)
Later can work but shifts emphasis: Ich hänge den Schlüsselbund an den Haken ... sofort. (possible, but marked / spoken style)

Your placement is very natural.

Why is the verb hänge in second position even though there are many parts after it?

German main clauses follow the V2 rule: the finite verb is in position 2.

Ich (position 1) + hänge (position 2) + everything else

Even if you start with something else, the finite verb stays second:

Den Schlüsselbund (1) hänge (2) ich sofort an den Haken ...

Is Schlüsselbund the same as Schlüsselanhänger?

Not exactly:

der Schlüsselbund = keyring / bunch of keys (keys together on a ring)
der Schlüsselanhänger = keychain/“key fob”/dangly attachment (the thing attached to keys, often decorative)

So in your sentence, Schlüsselbund is the whole set/bunch of keys.

Could I replace hängen with aufhängen? What’s the difference?

Often yes:

Ich hänge den Schlüsselbund an den Haken. (neutral, straightforward)
Ich hänge den Schlüsselbund an den Haken auf. / Ich hänge ... auf. (more explicitly “hang up”)

aufhängen is separable; in a main clause auf goes to the end:

Ich hänge den Schlüsselbund ... auf.

Both are common; aufhängen slightly emphasizes the act of hanging up.

Why is there no comma before neben der Tür?

Because neben der Tür is just a normal prepositional phrase modifying Haken. German doesn’t use commas to set off ordinary prepositional phrases. You’d typically only use a comma if you had:

a relative clause: ..., der neben der Tür hängt, ...
certain inserted clauses/phrases that require commas

Here it’s one continuous noun phrase: den Haken neben der Tür.

Could I say bei der Tür instead of neben der Tür?

You can, but it changes the nuance:

neben der Tür = specifically next to the door (spatially precise)
bei der Tür = by/near the door (more general vicinity)

If it’s literally right next to the doorframe, neben is the better match.