I am just a normal bitcoin user with little technical experience. I am not a programmer or something similiar. I know there a many possibiltys with technical experience. Is there a way I can automatically check this whole ton of bitcoin addresses?
Without some programming, i'm not aware of any option due to limitation from the website or server.
I have read a lot about that and people say there is a programm called Bitcoin Core that can do that for me? But how? That‘s the old wallet right?
Yes, Bitcoin Core can do that. It's not old wallet/software since it's actively updated. As for how, check this post
https://bitcointalk.org/index.php?topic=5452199.msg62221925#msg62221925. Although without a bit of programming, doing it thousand time would take long time. And that exclude the fact you need to download 600GB of blockchain.