Appologies - my description was kind of confusing.
In the meantime I found out, that both commands, "Do not auotomatically render subprojects" (42333) and "Prompt before automatic rerender of background subprojects" (42334) cause problems when creating subprojects.
When either of those options are set to on, the creation of the subproject seems to be incomplete: Instead of 4 (extensions rpp, rpp-bak, rpp-PROX, rpp-PROX.reapeaks) there are just 2 files created (the first two). This leads to (at least) two problems: The subprojects can not be opened from the "parent" project (by selecting the subproject track and hitting ctrl+alt+E) and the subprojects can not be saved or rendered (the mentioned error message, that the files can not be overwritten, is displayed).
Please check out this post (located in the development area) for a code example in a lua-script:
https://forum.cockos.com/showthread.php?t=210937