1. I had never been abroad before until I was 25. 

2. I met my best friend in HK in 2013. I had last seen her 2 years before. (Sounds strange)

It sounds better NOT to write in ___ in ____ in ____.

More natural: In 2013 I met my best friend in Hong Kong. That was the first time I had seen her in two years.

3. I have been to HK, which has very awesome night views late at night. When I got there arrived 1 year ago it had been raining a little bit. 

More natural: I remember the view of Hong Kong at night being amazing.  When I arrived a year ago (it was drizzling, but stopped soon after./ the city was wet from recent rains/ it was cold and rainy.)

4. I like to linger over a cup of coffe at the a very quiet coffee shop. 

“Linger over” sounds strange in this context.  “Savor” is better.

5. I need to do some excercise. Lately, I feel I am getting more lazier and lazier.

Notes:  Some of the sentences aren’t wrong, but sound strange…

When we use “had been”, it normally means that sentence is going to be an explanation for a later sentence.  If there is no explanation, it looks strange.

Ex: “When I arrived 1 year ago, it had been raining a little bit, (so….)

sentence practise

1. I had never been abroad before I was 25.

2. I met my best friend in HK in 2013. I had last seen her 2 years before.

3. I have been to HK, which has very awsome night views late at night. When I got there 1 year ago.,it had been raining a little bit.

4. I like to linger over a cup of coffe at the very quiet coffee shop.

5. I need to do some excercise. Lately, I feel I am getting lazier and lazier.

Well done! I don´t understand sentence number 2. If you say "I had last seen her 2 years before" that means that you saw her two years before you met her, which is impossible. What did you mean?