Garmin syncs automatically. With another watch, you can upload a .FIT file after each paddle.

Does the tide and wind adjustment work where I paddle?

Yes. It's worked out from your own GPS track, so it works on any water. It's most reliable on paddles that go out and back over the same stretch.

Is it in the app store?

No, it's a web app. Open it once in your phone's browser, add it to your home screen, and it works like any other app, notifications included.

Your sessions, yes. Heart rate, sleep and other body data stay private unless you choose to share them. You pick this the first time you open the app and can change it in Settings. On Monthly Coaching your workouts stay shared, because that's how your program is monitored.