Apple battery case phone battery draining first

I believe this is supposed to happen. It helps to maximize the total time you get from both the case and the phone batteries. iPhones charge relatively quickly until about 80% and then charging time slows down. The battery case would consume more power if it tried to charge your phone above 80%. I do not use the battery case myself nor does the product information tell you when exactly it begins to charge your phone, so I cannot give you specific numbers as to when it will begin to charge your phone, but it should at some point, probably well below 80%.

I think so... As long as the case charges your phone at some point you'll know it's working.

I've used external batteries with my phone and it's something like this: The external battery will drain maybe 25% to charge my phone from 60% to 80%, but will drain another 25% to charge my phone from 80% to 90%. Because you're using a battery to charge a battery, it is not direct. Apple engineers know what they're doing and have likely figured out the most efficient way to do this. If your phone stays at 100% until the battery case is depleted, you'll get less time from it.