I currently live in a metropolitan area, so no, I don't. I usually have a brisk walk until I reach the place I consider the starting point, as where I live it's not very comfortable to run, and it's not until then I start tracking the exercise.

Most of my friends who exercise also does it at places at least a couple of hundred meters away from their home. The ones that live outside the city, probably do start their run right outside their doors though.

Yes, that is common practice for some athletes. The Garmin Connect platform has pretty good privacy controls which allow users to hide activities or mask tracks near certain locations. Of course if Garmin gets hacked then all of the raw data could be exposed, but the same concern applies to smartphone platforms as well.