Is there a possibility to select all nodes (with selection rectangle) that are NOT part of any way? Maybe with filters?
Why do I need this? After deleting a way often tagged nodes remain existing. I can’t select the ways with all nodes in the first place, because this would also delete nodes which are part of multiple ways, thus damaging the ways that are not to be deleted.
You can use the search function
type:node ways:0
You probably also want to filter nodes which are members in relations, but I don’t know a simple method to find them, yet
Are you using JOSM Editor? If yes, than you can use these filters:
type:node untagged -child
type:node -child
More filters you can find on this website: https://wiki.openstreetmap.org/wiki/User:Mdelatorre#Searching_and_filtering
Thank you both, GerdP and Marek-M!
Both solutions work!
PS: It says JOSM in the thread title, but not in the text. Next time I will take care of that.
My fault because I did not check the subject of the post thoroughly. You have done everything so that I can fully understand your question. 
To start with a selection rectangle, add “selected” to your query.