What happens to my places if I sign out in the app?
The places stay on the phone, but the free plan limits apply to them: favorites become unavailable, and in history only the latest entries can be used. Nothing is deleted.
Everything you saved in your account is also stored on the server: after you sign in again, the data syncs again, and with Premium the entries become available.
When you sign out, groups are removed from the phone so they do not end up in another account at the next sign-in; they remain on the server, and the places themselves stay on the phone. If the device was revoked on the website, the app signs out by itself and tells you so — local data is kept in that case too.