Checking distances on the main scorecard screen or on the watch does not take any data.

Opening the map to check the layups means the map imagery is downloaded, unless it was viewed and cached already. The actual amount depends heavily on what user does - how much of the map area is browsed, at what zoom, etc. So there is no exact answer. A reasonable estimate is for browsing the entire course at default zoom is somewhere around 10-50MB (0.01-0.05GB).

If user is running the free version, downloading ads uses more data - like 1-10MB per round. There are no ads in Premium version.