Thank you Ernst!
I really struggle for some time with quality of my prints using Qimage, huge loss of time and supplies, tweaking every picture several times in postproduction to get it right, tossed many test prints in garbage bin.
Obviously, it starts when Mike incorporates Driver AI, which I was not aware of, as it has nothing to do with HP. I already decided to buy new printer, probably Canon. As a devoted user of a Z printers from time Z 3100 appear in 2007., you can see how desperate I was. Finally, I decided to go back to printing from other software, and find out that nothing is wrong with my printer, it is as marvelous machine as ever.
Anyway, your answer helps me. Actually, all my drivers setting was correct, but you make me thinking about AI Driver. So, I started to play with settings, and now everything is correct, again.
Driver AI was configured as in my first picture. I switch off all the controls and it gets a much better. Colors are now correct, but somehow pale. Printer Accounting confirms that test page is printed with 12% less ink than from Photoshop. Then I switch on „Always set driver print quality to highest available “, and test print comes out perfect, ink consumption is now the same as from Photoshop.