Unfortunately, busyness data is only available for certain stations (I believe it is limited to London Underground and Elizabeth line stations), and is not available for Wapping.
To answer your second question, you can access the full hierarchy of Wapping Rail Station at: https://api.tfl.gov.uk/StopPoint/910GWAPPING
By navigating the children properties of each StopPoint object, you can access child StopPoint objects and their naptanId properties. However, these will not allow you to access busyness information for this station.
despite the horrendously long URL, it defaults to showing crowding for Abbey Road so you have to reselect Wapping to get to the actual page
it wasn’t useful for my intended purpose (I wanted to compare the crowding level of two stations) because there is no vertical scale which incorrectly makes every single station look equally busy. I’m sure that’s not your fault at all, but it rather suggests that TFL is trying to hide something by publishing the information without any vertical scale.
there doesn’t seem to be a corresponding chart for Sunday
That seems very logical, except for the existence of a midweek chart supposed for Wapping as mentioned above.
Actually, no wifi at all – at least, not on some platforms on the Wapping line.