Dear Friend 1

You need to end sentences with question marks.

B. Nice. I've started a new activity in Milan.

"Nice" is an adjective; it doesn't apply to a question like "how are you doing", though some people will use it informally anyway. The correct answer would be "Well". Also "activity" is a little broad; I would use "business" here.
A. Great. What are you doing?
B. I opened an office in the city center for financial consultation.
A. What kind of consultation?
B. Crypto currency...
A. interesting... Is he it going well?

In English a business doesn't have a gender. You would therefore use "it" instead of "he". He would only be used for a person.
B. I've just started... I will tell you in some a few months.

You would not usually use use "some" after "in". You might use it in the future: "It was some months before he knew that the business was a success" or looking toward the future: "It would be some weeks before the package arrived."  You would not normally use it in the sense above though.
A. Ok... If you'll became become rich, please remember that you have a dear friend here..

"Became" is the past tense. "Become" is what will happen in the future. Also you wouldn't say "If you will become rich"; just if you become something.
B. Sure...what about you? Anna? Your baby? You told me that you would had let me know whether if you have had children.

"Had" is the past tense. Here you just want a straight conditional expression; "you said that you would let me know if (etc). "Whether" indicates whether or not the person currently has children. "If" means "If you have a child, then you will let me know."
A. I did! I sent you a message one month ago and Facebook was full of pictures.
B. Oh, you know that I can't use social networks.
A. You are a consultant in crypto currency and you are not able to use social networks??? Ah ah...

More a question of "don't want to" in my case. Try to avoid ending your sentences with ellipses (the three dots). It makes them sound like an incomplete thought. However on the whole this was a good effort; well done. I suggest that you study up on tenses (past, present, future, conditional, etc); they seem to be the area where you're having the most trouble. The rest of it is fine.

Dear Friend 1