The building is a three-storey block built in 1964, but next year it’s going to be demolished to make way for new multi-storey apartment buildings. The building is a three-story block built in 1964, but next year it’s going to be demolished to make way for new multi-story apartment buildings.

The building is a three-storey block built in 1964, but next year it’s going to be demolished to make way for new multi-storey apartment buildings. The building is a three-storey block built in 1964, but next year it’s going to be demolished to make way for new multi-storey apartment buildings.

If you are learning British English, "storey" is correct here. If you are learning American English, it's "story."

I only found this out shortly after moving in (from a neighbour), and I was really upset that my landlady hadn’t bothered to tell me. I only found this out shortly after moving in (from a neighbour), and I was really upset that my landlady hadn’t bothered to tell me.

I might suggest removing either "shortly" or "only," since they temporally contradict one another. "Only" exaggerates the length of time between when you moved in and when you heard of the building's demolition, whereas "shortly" compresses that length. While not necessary, removing one or the other could lend clarity.

I only found this out shortly after moving in (from a neighbour)from a neighbor only after moving in, and I was really upset that my landlady hadn’t bothered to tell me. I found this out from a neighbor only after moving in, and I was really upset that my landlady hadn’t bothered to tell me.

Use of parentheses here is fine if you're texting a friend, but in any other situation it's better to reword the sentence instead.

It takes me only 15 minutes to get to my work by bus, and on my way back, my colleague gives me a ride since he lives nearby. It takes me only 15 minutes to get to my work by bus, and on my way back, my colleague gives me a ride since he lives nearby.

It takes me only 15 minutes to get to my work by bus, and on my way back my colleague gives me a ride since he lives nearby. It takes me only 15 minutes to get to my work by bus, and on my way back my colleague gives me a ride since he lives nearby.

You should use a comma before "and" here because it's connecting two complete sentences.

So tThe whole waytrip rarely takes me more than 30 minutes. The whole trip rarely takes me more than 30 minutes.

Alternatively, you could combine this clause with the previous by using a conjunction like "so." For example, ...my colleague gives me a ride since he lives nearby, SO the whole trip rarely takes me more than 30 minutes.

So the whole waytrip rarely takes me more than 30 minutes. So the whole trip rarely takes me more than 30 minutes.

But what I’ve come to love most is the courtyard., But what I’ve come to love most is the courtyard,

Even though mMy first impression of it, however, was far from perfect. My first impression of it, however, was far from perfect.

This rephrasing makes it clearer that you are moving to explain a not-so-great first impression. It also makes it a complete clause.

Eeven though my first impression was far from perfect. even though my first impression was far from perfect.

This is just my opinion, but I think it sounds more natural to connect these two sentences.

That stripe ran straight and then branched out to each entrance. That strip ran straight and then branched out to each entrance.

That stripe ran straight and then branched out to each entrance. That strip ran straight and then branched out to each entrance.

Between the branches, flowers were supposed to be growing, but I honestly I don’t remember if there were any that day. Between the branches, flowers were supposed to be growing, but I honestly don’t remember if there were any that day.

As far as I could tell, it suited me in every way: the location, the rent, the fact that cats were allowed, and a. All the rooms were even furnished. As far as I could tell, it suited me in every way: the location, the rent, the fact that cats were allowed. All the rooms were even furnished.

"All the rooms were furnished" is a complete sentence, while "the location, the rent, the fact that cats were allowed" is a list of nouns and one phrase that functions as a noun. Therefore it's hard to make a list with all four of these items in a way that sounds natural. I think it's better to separate the last one, and emphasize it with the word "even."

The playground has new monkey bars, (which I use to train my grip strength), and a square sandbox, though I’ve never seen a single child playing there. The playground has new monkey bars, which I use to train my grip strength, and a square sandbox, though I’ve never seen a single child playing there.