The ExcellGrowth app uses proven Apple security and privacy frameworks to keep your data private, secure and completely under your control. See Apple's documentation on iCloud security and privacy
The app stores your data on your device(s) and in iCloud by default. This enables you to back up your data, share it between your Apple devices (if you have more than one) and to change devices easily (e.g. upgrading to a new iPhone).
All your data in the ExcellGrowth app is stored in your iCloud private database, which means that it is subject to the same level of security and privacy Apple provides with other personal data you store in iCloud (e.g. photos, notes, files, ... ) and the developers of the ExcellGrowth app don't have access to any of it.
If you prefer to store ExcellGrowth app data on your device only, and not use iCloud, you can go to Settings on your device, select iCloud, scroll down to ExcellGrowth and switch the toggle off.
It is possible for you to share your screen during a FaceTime call (e.g. with a coach) but you have to deliberately enable this during the session. You can choose if you want to do this or not, and which views of the ExcellGrowth app to show during the call.