in the meantime I have made progress: I had the steering readjusted (the first adjustment was done poorly) and now the steering wheel is centered, but the steering is still a bit nervous, the car runs after each and every groove. According to the adjuster, there is a bit tolerance in the front suspension arms/bushes.
According to my Jag specialist this is more or less normal, they would probably do another 100K km before TUV would complain, but it's not like new any more (of course after 24 years). We also tested the engine mounts (open the hood and do a little bit of braking) and they are clearly finished. So the next task will be to change the engine mounts - and when the front suspension is already lowered/out, we'll have the bushes/struts renewed, too. I hope this will also stop the steering wheel trembling, though I have learned that the steering column also has mounts/bushes that wear and that are even more difficult to change.
Finally I also found out what that strange noise is coming from - it's the radio! Who would have thought that, but when I turn off the radio that annoying whistling noise above 100km/h is gone. The specialist also gave me a kind of explanation but I already forgot it