There iIt has a balcony attached to the bedroom.

Apartments usually have more than one room, and since you haven't mentioned if it's just a one room apartment, you'll need to mention a particular room. Also... narration-wise, you can add a bit more detail about the balcony, like "a balcony with a great view", or "a 3-ft wide balcony", since just mentioning the balcony for the sake of it seems awkward.

Two years have passed since I moved here.

I like this roomplace, but yesterday, an annoying person seemeds to bhave moved to my next-door room.

The neighbor's alarm went off at 2 a.m. and continued sounding until 4 a.m. aAnd what i's worse, is the person often hity often kept hitting the wall.

Again, the alarm went off at 2 a.m. I got so angry that I went out and knocked the door of the neighbon my neighbor's door.

No one replied.

You could also say, "Nobody replied" or "No reply".

I camewent back in my room and hit the wall with anin rager.

Then, the neighbor hit back the wall muchback even harder.

I got furious, so I kicked the wall, yet the neighbor didn't stop hitting back.

It's a bit unclear what "it" here is, is it about just hitting once often? Or is it about hitting back every time the protagonist hit the wall?

I gave up and listened to the music with my headphones on.

Morning has comes.

I called the real estate management company on the phone and complained about the neighbor.

"On the phone" is unnecessary here.

Then, he said wonderinglyin confusion,

If you meant to say 不思議そうに, then this is right. Wonderingly, I think, is used to mean 魅了されて.

"IThat's strange because n. No one lives in that roomapartment.

We don't have any contract with anyones for that roomone.

Maybe you've mistakenook it for what the resident on the floor below you did?

"Impossible! I shouted,

This sounds more natural.

Absolutely someone isSomeone is definitely in the next room!

Then, the staff then said,

Just making it sound a bit more natural.

"Okay, I goet it.

I'll check through security cameras to see if someone tresspassed into the roomplace.

I was lookinged forward to ahis call from him.,

I got aAnd he called this evening., saying,

"We've checked outthe footage and found no one broke into the room.

Using just "checked out" would by like using the idiomatic phrase, which means leaving a hotel after staying.

Also, we actually entered the room actuallyapartment today, but we couldn't find anything like an alarm watchclock or a mobile phone"

I thought they cut corners at their investigation.

Not sure what you meant here, but TLing cutting corners in investigation directly would be, "行き届いていない調査をした” or ”雑な調査”. It would mean that they did at least 80% of the work, but didn't do the rest of it properly. But from the sounds of it, it looks like they didn't perform the investigation at all, since they searched an empty apartment and didn't find anything.

I'll get any evidence by myself!!

I bound a mirror on the stick fora selfie-stick.

When the alarm started, I went out to the balcony and sawfound the room lights on.

As I expected, someone should beit meant someone was there!

I stretched my arm with the stick and looked into the room through the mirror and, but found no one was there.

I also found tThe window was unlocked.

Probably, the management company's staff forgot to locking it and turning offleft the lights on, too.

I put my phone into a the pocket onf my jeans to take photos of evidence.

I bound thetied one end of thea rope on the fence of my balcony and bound the other end on myself.

I jumped ionto the balcony of the next room.

I entered the roomapartment and hunted all over the room for the alarm, but I couldn't find it.

When I looked back to the window where I entered, I wasbecame aware of how the outside was different from the onewhat I always seeaw.

I went out to the balcony and saw the darkness, all overenveloping the outside.

There should've been some buildings in front of ourthe apartment, but there was nothing is there now.

I caouldn't see anything but darkness.

You can switch tenses in Japanese during narration, but we keep it all in the same tense in English.

I turned towards my room but it had disappeared and left the darknesstoo.

I turned to the otherpposite side.

It' was the same.

Even thoughwhen I lookinged up and down, I just learned it's was just darkness.

I wentheaded to the entrance door and opened the door.

The corridors had disappeared and became darturned black.

Just writing "dark" here would make it seem that the corridors had dimmed in brightness. Black would be a better word here.

LIt looksed like I'm was in a room floating in an endless outer spacevoid.

The rope from my balcony had disappeared.

I caouldn't go back to my room, to the real world.

I took out my phone and tried to calling someone, but couldn't.

I haveThere was no signal.

I was at a loss for what to do and so, seated myself on the floor.

Suddenly, the alarm of my phone soundedrang.

It's sSix o'clock.

I usually geot up around this time.

Tears coame out in despair.

Why had I caome here for such a trivial thing?

I should've ignored it and moved to another room.

Is "room" here just 部屋 or アパート?

The alarm waskept sounding continuously.

RescueHelp me!

Rescue me, sounds like you are ordering someone.

I hit the wall harder, and then,... the person hit back much harder.

RescueHelp me!!

I continued hitting the wall, but the persony stopped hitting back.

Please rescue me!!

This is okay since you are using please.