Regarding Coolant pumps running while car is idle. So, as some of us have noticed, the coolant pumps run a lot more than they used to. This seems to be related to State of Charge (SOC) and other factors. It also happens after charging even when I have a relatively cool battery. I also notice the coolant pumps run at a higher %, i.e. full blast when driving the car and the battery is relatively cool.
My uninformed wild guess is that it's not doing it to cool the battery at all. Rather it is just to confirm cell temp uniformity. The BMS on the older batteries like mine only has temperature sensors on two cells per module. One glued to a cell near the coolant inlet and near the coolant outlet. So the BMS doesn't have a picture of cell temps in the rest of the module, say the middle of the module. My guess is that Tesla found a situation/condition where a cell, (a bad cell perhaps) is getting hot and the BMS doesn't know it. This condition would be possible if the coolant pumps were idle, thus the hot cell would not dissipate heat to the rest of the module very well. So to mitigate they run the pumps continuously where there is any possibility of this happening. This allows the BMS to have a good idea of the whole module temperature, as long as the pumps are running. Those conditions are high state of charge, charging (even AC charging with a relatively cold battery), and driving. Perhaps other conditions as well.