Meine Freundin schließt den Reißverschluss langsam, als würde die Jacke gleich wieder kaputtgehen, und hängt sie dann auf einen Kleiderbügel.

Because Reißverschluss is the direct object of schließt. In German, a masculine noun changes from der in the nominative to den in the accusative.

So:

• der Reißverschluss = the zipper as the subject
• den Reißverschluss = the zipper as the object

Here, meine Freundin is doing the action, and den Reißverschluss is receiving the action.

Reißverschluss means zipper or zip fastener.

Literally, it is made up of:

• reißen = to tear
• Verschluss = closure, fastening

But you should learn Reißverschluss simply as the normal word for zipper.

Yes, einen Reißverschluss schließen is a very normal way to say to close a zipper or to zip something up. German can also use zumachen in some contexts, but schließen sounds very natural here.

Here als means as if.

German often uses Konjunktiv II for unreal comparisons or impressions, and würde + infinitive is a very common way to form that. So als würde die Jacke gleich wieder kaputtgehen means something like:

as if the jacket were about to break again at any moment

The speaker is not saying the jacket really will break. It is just describing how carefully she is closing it.

This is a special pattern used with als in unreal comparisons.

After als, German can use a verb-first structure with Konjunktiv II:

• als würde die Jacke ... kaputtgehen

A very similar alternative is:

• als ob die Jacke gleich wieder kaputtgehen würde

Both mean as if the jacket were about to break again.

So the verb-first order after als is normal here. It is not random.

This part can be confusing because each word adds something important:

• gleich = soon, any second, right away
• wieder = again
• kaputtgehen = to break, to stop working, to become broken

So gleich wieder kaputtgehen means:

to break again any moment now or to go broken again right away

Here gleich does not mean equal. It means something like very soon.

Because kaputtgehen is a separable verb.

Its dictionary form is written as one word:

• kaputtgehen

But when it is conjugated in a main clause, it usually splits:

• Die Jacke geht kaputt. = The jacket breaks / goes broken.

With würde, the infinitive stays together:

• würde kaputtgehen

So in your sentence, kaputtgehen stays together because it is an infinitive at the end of the clause.

Sie refers to die Jacke.

That can be confusing because English would say it, but German uses grammatical gender. Since die Jacke is feminine, the pronoun is sie.

So:

• die Jacke → sie

Here sie does not mean she. It means it, referring to the jacket.

Because the subject is the same as in the first clause: meine Freundin.

German often leaves out the repeated subject in a second coordinated clause with und when it is already clear.

So this:

Meine Freundin schließt ... und hängt sie dann ...

is short for:

Meine Freundin schließt ... und meine Freundin hängt sie dann ...

The omitted subject is still understood to be meine Freundin.

Because auf is a two-way preposition. With these prepositions, German uses:

• accusative for movement toward a destination
• dative for location

Here the jacket is being moved onto the hanger, so German uses the accusative:

• auf einen Kleiderbügel

If you were just describing where the jacket already is, you would use the dative:

• Die Jacke hängt auf einem Kleiderbügel. = The jacket is hanging on a hanger.

It is the same basic verb, but German distinguishes between:

• transitive hängen = to hang something up
• intransitive hängen = to be hanging

In your sentence, meine Freundin is doing something to the jacket, so it is the transitive use:

• Sie hängt die Jacke auf einen Kleiderbügel. = She hangs the jacket on a hanger.

This can be tricky because in the present tense both forms look the same:

• Sie hängt die Jacke auf.
• Die Jacke hängt am Haken.

The difference becomes clearer in the past:

• Sie hängte die Jacke auf. = She hung the jacket up.
• Die Jacke hing am Haken. = The jacket was hanging on the hook.