I don't think so unfortunately, since programs with already existing rules run just fine. It seems to be specific for programs without any rules for them. No matter if I simply delete an existing permit rule for stuff like Thunderbird or Chrome, or if I try some new software I have never used before (SmartFTP instead of FileZilla), no popup dialogue appears and they just can't send/recieve anything.
Strangely enough, if I uninstall und then re-install ESS, everything works just fine for an hour or so. Then without any notable change or discernable reason, it turns back to the situation mentioned above.
Nonetheless, I'm going to give your solution a try now and hope for the best And of course, thanks for the effort so far!