After the AC has been used, the car might continue (30mins?) running the fan to dry the evaporator coil. That's normal.
The target temperature for battery heating when conditioning the cabin has changed over time I think. It might be around 70F maximum. Most probably your battery is already at 70F in the morning these days. The target battery temp might be even lower than 70F, I don't remember and am not in my car right now. You would need to use ScanMyTesla to verify.
Similarly, the target temp for supercharging might have changed. I'm under the impression it was around 40-45C (104-113F) the last time I supercharged, but I'm not 100% sure. Again, if the battery is warm enough, it won't do anything.
Unless you are seeing inexplicable slow supercharging, I would presume the BMS is doing its thing as intended and wouldn't worry.