This year, I have read more than 200 books which areis my record ofor reading in a year. This year, I have read more than 200 books which is my record for reading in a year.

I'm guessing that you mean that this is the most books you have read in a year and corrected it to mean this Well done by the way!

This year, I have read more than 200 books which areis my record ofnumber of books read ing a year. This year, I have read more than 200 books which is my record number of books read in a year.

I changed the way toI read books, from understanding all of the contents to only searching for topics what I am interested in. I changed the way I read books, from understanding all of the contents to only searching for topics I am interested in.

I changed themy way tof reading books, from understanding all of the contents to searching for topics wthat I am interested in. I changed my way of reading books, from understanding all of the contents to searching for topics that I am interested in.

OnFor (in) certain parts, I read deeply, sometimes I write down the sentences oin my notebook. For (in) certain parts, I read deeply, sometimes I write down the sentences in my notebook.

You could also say "sometimes writing down sentences in my notebook." which sounds even better. Nothing wrong with what you have written however.

On certain parts, I read deepintensively, sometimes I write down the sentences oin my notebook. On certain parts, I read intensively, sometimes I write down the sentences in my notebook.

"Intensively" might be a better word in this context.

On the plus side, I can read many topics onin a short period. On the plus side, I can read many topics in a short period.

On the plus side, I can read many topics onin a short period of time. On the plus side, I can read many topics in a short period of time.

The mobiggest benefit of this way is that my summarizing skill ihas improved. The biggest benefit of this way is that my summarizing skill has improved.

When talking about the results of an action taken in the past it is best to use "has" rather than "is"

The mobiggest benefit of this way is that my summarizing skill ihas improved. The biggest benefit of this way is that my summarizing skill has improved.