Not "a lot" but 3 points (stated in the Privacy Policy): ping once a day (HockeyApp), OS version+language once a month, and opt-out uncategorized hosts/apps submissions.
I don't see how it's not private and "misleading".
Every domain you visit and every app you have installed is a lot of information. Information I don't want to share, even 'anonymously'. (It would be trivial to deanonymize that data)
If you claim your app stores data locally, it better not share data like this. Otherwise your marketing copy is just the usual horseshit.
No way, we are not collecting this because we don't need it (and yes, it would be not very private). I probably should improve the phrasing in the Privacy Policy.
Qbserve detects popular apps and sites automatically by matching them to the entries in the bundled database. If it can't find a match, it puts the app/site into "Uncategorized" category.
Then when the user decides to assign it to some category, there's a checkbox with text "Submit domain + category" and hint "Send it to developers to improve Qbserve". You can disable this checkbox forever in the app's settings.
Then we get somethings like { "host":"ycombinator.com", "category":"news" }, check if this site is really popular and add it to the bundled database in the next update.
I don't see how it's not private and "misleading".