Funny how fuzzy my memory has become after answering some of these questions. I'll do my best! Most of this could be measured.

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1. I believe battery heating began below about 5C. I also think Battery Cooling kicked in around 30 or maybe 35C. Anytime vehicle is powered on, or plugged in.
2. Again, a little fuzzy on exact details here, but I believe battery conditioning is active during charging and for about 3 days after end of charge. Fairly low power if battery is already within limits when the vehicle is plugged in. Better for battery life, etc.
3. No.
4. There is inherent buffer in the battery "fully charged" and "fully empty". Voltage is dependent on temperature, charge/discharge rate etc.