I have a serious question. If we come across mold in the apartment which we rented and prompltly communicated with the landlord about this issue.
And is it right he can force you to pay all the cost to clean (with the help of specialist who also owns a certificate for dealing such issues).
Legally who will pay? Tenant or Lardlord in Berlin, Germany?
The strong answer would be much helpful...

It is not easy to answer who is responsible for the mould. Mould usually appear due to poor heating and ventilation. There may be other causes like Water leaks from windows, roof, guttering, internal plumbing and flooding. You need to analyse whether it is happening due to your life style or problem with the apartment.

if you are sure it is not your mistake, you can ask a specialist to do a kind of tempereture test over time. He will measure the outside wall temperature, the inroom wall temperature and the inroom air temperature. From this measurement, one can know for sure if it is a lifestyle problem (no proper heating or no proper umluftung -> then it is your problem) OR the themal isolation of the building is so bad that caused the mold.

Of course, the löser has to pay for this things.

Talk to the Hausverwaltung and your Neighbours to see if anyone else has the same problem, or if the Flat has had those problems in the past. Also, did you put some big furniture too close to the external wall?