Hello ralfhauser, welcome to the Spotify Community!
The way to invite people would be the following:
1. Go to----People---Everyone----Filter (whoever you wand to invite)
2. Send your friend whatever song you will like! The person will receive this and have the option to use Spotify for listening to the track you sent it :)
I really hope this helps.
ps: you have to link to your Facebook for showing the image on Spotify. One is linked to Facebook that doesnt mean you show your music, you can always use the Private Session option. No one but you will know what you are listening to.
I forgot something..
There is already a link to the help section on Spotify.
Go to "Help"---there you will have the option to go the Spotify Help Section or Community.