So, after a lot of iterations of auto-node-move i managed to bring the quality up to 0.043514615. When it comes to the surface mesh size, on the problematic areas the cells have the size of around 5, but there are areas where the face size is near 3 and the problem persists. For the first cell height i have for different zones from 0.01 to 0.08.
Regards,
Piotr