But I noticed, that if I check the Option "let armory run ... in background" then I have a process "bitcoind" running.
But if I uncheck the armory option mentioned above, run bitcoin-qt wallet along with armory, this process is not there, and armory just doesn't do enything - progress bars stay empty and no spinner whatsoever is there.
My Question is - can it be that the "RPC server" is the bitcoind process and that it isn't running?
If your setup is working, don't change anything - if you're having trouble it'd be best to start your own thread, as the problem isn't fixed here yet.
That said: When Armory is configured to manage Core, bitcoind is run in the background. This, as you suspected, provides a RPC server for Armory to query.
Sometimes something gets tripped up when Armory is configured to manage Core, and hence my suggestion to Marla_H.
In this situation, and without bitcoind, Bitcoin-qt can also provide a RPC server for Armory, but requires some config - which I apparently should have given in my last post. (Sorry!)
This can be done either by adding the following to a text file named bitcoin.conf in your Bitcoin Core data directory:
server=1
# Accept Incoming
listen=1
Or adding the following to the end of your Bitcoin qt/Core shortcut: