I met an American middle-aged man who lives in Arizona State on a website.

Normally when we name a state, we don't say the word "state."

He said that he hadoesn't been usinguse Twitter, Facebook and other similar social platforms.

"He doesn't use" or "He hasn't been using ... lately / recently / this past week."
Normally when using the present perfect continuous ("hasn't been using") it makes more sense to anchor it to a time period ("since last Friday", or "recently".)
But in this context, I think present continuous ("doesn't use") makes more sense, as it sounds like a general sentiment.

I agreed with him that we both believe the words on the main social platforms are actually dominated or led by some political group.

"I agreed with him that we both believe" -- redundant.
"I agreed with him that" OR "We both believe that" but not both

I expressed my own idea that it's will be normal for people in just in 20 years, some of us would to be compulsorily implanted with electronic chips for some reason.

Additionally, he surprised me by thinksaying that all the healthcare was free in my country, h. However, it is not.

"thinking" makes it sound like you can read his mind. "Saying" makes it clearer that he said these words out loud.

I met an American middle-aged man who lives in the state of Arizona State on a website.

He said that he hasn't been using Twitter, Facebook, and other similar social platforms.

I agreed with him that we bothWe both agree in the believef the words on theat posts on main social platforms are actually dominated or led by some political group.

I expressed my own idea that it's normal for people just in 20 years,about how I believe that in 20 years, it would be normal for some of us wouldto be compulsorily implanted with electronic chips for some reason.

Additionally, he surprised me by thinking that all the healthcare was free in my country, however, it is not.