Ok, I made some progress!
First, I opened the HDD and took out the latch mechanism - is it supposed to be taken out freely with tweezers? Strange... I made a dust cover and tried to spin it one more time. And this time I was able to mount two drives! Wow, that was a huge surprise. I look around and found calibration data, which I would say is a 50 % of successes. Now if I get new HDD image, I will copy my files.
But, before that, I wanted to clone this HDD. With many different freeware programs. No luck this time, as the HDD started to read and then parked multiple times. So my previous fix was either a luck, or I accidentally made head/disks alive once again. Nevertheless, I kept trying and almost paid 30 $ for software which can skip bad sectors during copying.
But, once again I was lucky and found DDrescue with GUI for 5 pounds. With this guy I rescued 270 MB reading forward and around 6 GB backwards! Not bat I would say, but now HDD seems completely dead, just like in the beginning. So now I will open the lid once more time and try to do "my magic". I mean I will open and close it. Maybe later on I will blast some air from can. Will see.
All in all, I am quite happy with all the steps I done. Also quite surprised how durable HDD might be. Cheers