Do you put your phone on charger daily? The same concept: put it on the charger while you are sleeping, even if you have not drained the whole battery. With PHEVs and EVs, there is the unofficial rule called "ABC" (Always Be Charging), as "shore" power allows the battery management system to condition the battery either by cooling or heating it without using battery charge, but power from the outlet. Not to mention cabin temp pre-conditioning function, which is very nice on very hot days (in my case) to come to the car that's not a scorching hot oven(especially if you are connected to some free public charger).
It really depends. I’ve seen the charge level drop while connected to power but not actively charging. A Model 3 shows that it’s accepting 2V at 0A. I think for the most part it’s operating off of the battery.
The only time I’ve seen it not charging but providing substantial power was during preconditioning. I saw it displaying about 240V but 13-18A. I think turning on A/C or heat can also do that.