Re the safety: the issue is that if the wiring is not in tip top condition, the high current draw over many hours can cause overheating. A socket intended for use for EV charging is supposed to have a dedicated circuit and a particular sort of safety device at the consumer unit. Since the accommodation doesn’t advertise EV charging, you can guarantee this won’t be in place.
Chances are it will be absolutely fine, but at a minimum I would eyeball the wiring, make sure there are no other high-power items in use (to the extent that unless I was certain the kettle was on a different ring main, I would turn the charger off to boil the kettle) and check the plug for warmth several times over the first few hours.
I would also ask permission and offer to cover the cost.
33kw is how much their battery can hold when it is full. 7kwh is how many kw the charger can put into the battery each hour.
180 degrees wrong, I’m afraid. kWh is a unit of energy. 33kWh is the amount of energy the battery holds. It’s the amount of energy you get if you charge at 1kW for 33 hours, or 3 kW for 11 hours, or 33kW for 1 hour.
kW is a unit of power, or energy per unit time. 7kW is the speed with which the charger can put energy into the battery. A 7kW charger will add 7kWh in 1 hour, 14kWh in 2 hours and so on. Filling a 33kWh battery would take a little under 5 hours.
(Actually a bit longer, because charging is not 100% efficient, but ignore that for now.)
So we have a 77kw battery and a 7kwh charger so it would take 11 hours to charge our battery from completely empty to completely full (77/7 = 11).
You have a 77kWh battery and a 7kW charger, but yes, 77/7 = 11.