Rear cassette shifting I replaced my free hub body due to pedal slippage. I also replaced rear cassette and chain for regular maintenance. Since then the problem started and I replaced shifter and cables as well as rear derailer. I am out of ideas. I know how to properly set high and low range and adjust index. Once the index is set for gears 8-4 or so, gears 3-1 shift too quick and the chain ends up in the large ring when the shifter says it’s in 3 or 2 and the last shifts to 2 or one are incredibly tough as the cable is so tight. If I loosen the cable to allow a smoother shift in gears 1-3 gears 6-8 don’t work together.

The rear cassette and chain is 8 speed, the same part number as previously installed.
You have an SRAM X4 8-Speed shifter. The description says: 


  Featuring our proven ergonomics and award-winning 1:1® Actuation


and adverts in e-shops say:


  Compatible with ESP (1:1 ratio) rear derailleurs only.


The pull ratio for Shimano rear derailleurs is 1.7. It is not compatible. You need a different shifter or a different rear derailleur (like the X4).