We get notified whenever add a new activity in Strava, and thus, the sync button usually does not find anything. If you are missing something and you are a Pro user, you can use our Historic Sync feature or contact us.
Yes, by toggling the Prefer Private Activities on your Settings, we will automatically mark activities uploaded to Strava as Private.
Strava remembers that you deleted the item and will not allow us to upload it again. To work around this, select the item from the Stream, selected the (Export) icon and download the TCX file and manually upload this to Strava.