Hi

Can you in any way make a fill method to get the stiches 90 degrees contra the contour? (something like in the attachments)

That would be an S-stitch (how appropriate). Have a look over here: https://inkstitch.org/docs/stitches/s-stitch/

You build it up just like a satin stitch, then set method to S-stitch, maximum stitch length to your needs and split method to staggered. Define a value for Stagger this many times before repeating.

Thanks. But in my installation of inkscape and ink/stich the alternative "S-stich" is not available. May I have to old version? Or may it be some other setting I need to do to make "S-stich" appear in the list?

I suppose you are on an older Ink/Stitch version. S-Stitch is part of the latest release.