Do you want to track the aircraft or just want to know what is inbound/outbound from your home airport?
If you are wanting to track them, for the most part, it won’t happen. (check the FAQs for more info on this). As far as just knowing inbound/outbound, some airports work when the flights are filed IFR and are going to/from the US. Granted (FA gurus correct me if I am wrong), the arrival/departure times may be off due to when the US controllers hand the aircraft off to international controllers.
i just wanna know if there is somewhat expected at my home airport,
especially General Aviation flights. We have sometimes flights from
the US (airports like KSWF,KBGR) with G4s, G5s and Falcons and
some more. And what i want to know is, are they shown if i click on the
arrivals list for my home airport (which is EDDF in Germany) ?
Actually this page should be more what he wants. It should show enroute or scheduled GA flights, but sometimes unknown air carriers are grouped in there too.
Basically, the only GA activity you can track is that which is coming from or going to North America from EDDF. I do believe that Frankfurt does provide a live feed for arrivial and departures.