The second attempt: I took whole movement apart again, cleaned it, oiled it, I also managed to clean all of the jewel holes with pegwood. I also opened mainspring barrel and took out the mainspring. It was quite dirty, I cleaned it, oiled it, and put everything back again.
To my surprise, the amplitude looked very good, the automatic winding system seemed fine. The last step was to put the movement in the case. I had trouble with the dial ring and putting stem back (although I think I put it correctly). I took the movement out of the case to check for a problem, but then the amplitude got lower and the watch completely stopped.
Since I did not move or touch anything, I suspected it was the mainspring with not enough energy. I gave "external" power by using pegwood and slightly touch the central wheel. The amplitude was normal again.
So, my conclusion would be that I have problem with the mainspring: it does not give enough energy for the train to transfer it to the balance wheel. Maybe at first, when the mainspring is fully in tension, but after some time, it is just not enough and watch stops. However, I am not sure where I can buy new 7009 (or 7s26) mainspring for replacement.
On the other hand, it could be that the hole made for the barrel arbor got bigger, and now the mainspring teeth are not fully in contact with the center wheel. But I would say that the problem is the mainspring. It is strange however that the watch stopped few days after it fell on the ground.
You are correct, I use polident denture fizzy tablets which works well. I have also used an ultrasonic cleaner with a cleaner I mix up. You will never get the hairline cracks completely but you can get them to be way less noticeable.