Now I live in my hometown –My hometown is a small province located in the north of Vietnam. This is where I'm living now. / I live in a small province located in the northern part of Vietnam.

If (my) memory serveds me right, when I was a kid, I lived in a small village with my family.

Until 8 years oldI lived there until I was 8 years old, about 8 years ago, when my family decided to move to the city. / About 8 years ago, my family decided to move to the city.

It was hard to get used to living in a crowded place when I still was a child at that time because in my village, I had many friends around me. / As a child who had many friends around me, it was hard getting used to living in a crowded place.

Every day, I liked to go to their house to play with them together.

But now, due to (our) hectic schedules, I cannot regularly keep in contact regularly with them anymore.

At present, I want to live in a city similar to my hometown because of 3 advantagereasons.

There are many shops, restaurants, and supermarkets where people can buy luxurious, beautiful, and suitable things for their choiceneeds.

Since you stated the exact number of reasons in the sentence above, I think it'd sound more natural if you listed the reasons out.
Ex: One, there are many shops. Two ...etc

My hHometown [1]

Capitalization for title

NRight now I live in my hometown – a small province located in the north of Vietnam.

You can say "right now" or "at the moment." When you say "now" it implies a change. For example: I was living in Tokyo, now I live in Paris.

If my memory serveds me right, when I was a kid, I lived in a small village with my family.

It was hard to get used to living in a crowded place when I was still was a child at that time, because in my old village, I had many friends around me.

I would say "old village" or "last village" to clarify and differentiate between the new town/city

Every day, I liked to go to their house to play with them together.

At present, I want to live in a city similar to my hometown because of 3 advantages.

I've been taught that it's generally better to spell out numbers if they are less than ten in normal sentences, for example to write instead "because of three advantages." However, you are not wrong here and it's just a tip.

There are many shops, restaurants and supermarkets where people can buy luxurious, beautiful, and suitable things forin their choices.