To import a workout to Zwift from TrainingPeaks, you will need to export it as a .ZWO file rather than a .fit file. TrainingPeaks provides instructions on how to do so here.
Only power cycling, RPE, and distance based pace workouts can be exported as .ZWO; so a heart rate based workout will not be compatible.
After exporting the .ZWO from TrainingPeaks, you can import it to Zwift by following the steps in this article.
After looking through the Garmin Forerunner 935 manual, I found that it can be used as a heart rate monitor in Zwift. To do this you will need to enable heart rate broadcasting in the watch’s settings.
The Forerunner only broadcasts heart rate data over ANT+ protocol though, which is not compatible with iOS devices directly. However it is possible to connect an ANT+ device to iOS using a signal bridging device. You can find information about that in our ANT+ article.
As for tracking your training success; while bike computers like the Garmin 820 are not compatible, Zwift offers many of the same features that a bike computer would.
All of your ride data will be displayed in real time on the in-game HUD, and will also be recorded and saved at the end of your ride in the form of a .fit file. You can even have the .fit files automatically uploaded to third-party sites, like TrainingPeaks.
Your FTP will also be automatically updated at the end of each of you rides.
I hope that I was able to point you in the right direction. And if you ever run (or ride) into any roadblocks getting while everything set up, please feel free to submit a support ticket; we’re always happy to help!