I'm guessing that's part of how it works. Perhaps we can't consider DMs private? Perhaps the contents are though, did you try to read a DM? The rest, yeah, those are public events, so yes, if they have your public npub, they can view all the events as if they were you, but they can't sign anything...

The notifications and your feed are not concerning, that's a feature. You can check what other users are seeing in their feed, which is pretty cool. For the direct messages, yes, that's concerning. Afaik there is some solution (was it giftwrapped messages?) that not all clients support yet. Which ...