So I went to the Expert meeting (in Apple reseller store this is equivalent of Genius I assume) and they took my iphone for a 5 days checkup.
After 5 days they called me to come to take my iPhone saying that they checked everything, even talked with Apple itself, and the problem is only in my sim-card and I should take it (physically, not just by phone assistance) to the carrier.
They also told me that when they put their own sim-card (which was even of the very same local carrier) in my iPhone, the iMessage worked fine but when they switched it again to my sim card it again did not work (everything with their own AppleID so there is no problem regarding AppleID here).
So I took my iPhone I logged in with my AppleID. Suddenly everything worked fine. iMessage and FaceTime (and even the option "Text Message Forwarding" to my MBP worked and a number showed, for the first time.., on my MBP to verify send and receive message from the iPhone).
So, eventually something solved the problem. I don't know exactly what but maybe some "rattling" to the device made it (taking out the sim, putting other sim, putting again the sim, in the process I also changed my AppleID password after giving the iPhone to the reseller.)