Indeed. The car will not power up when the 12 volt auxiliary battery is flat as you have seen, even when here is enough charge in the high voltahe battery. All the car electronics run from this small battery. When the car is powered up, the high voltage battery will start charging the 12 volt...
1 should be fine
2 that is your own choice. Personally i would rex the fast parts also on the way out. So 50/50
3 you will loose about 25% range in winter. But preconditioning before departure from home when plugged in helps.
4 yes your commute will mean refill every day.
5 dont know about cost...
It sounds to me the charging unit in the car is shutting down because of overheating. If you do it on low it is not getting as hot and ccs does not use the in car charging unit.
You need to check if the price is including or excluding the OLEV grant. 175 is about right if it includes it. As you have bought a second hand car you need to check if your car is still elegible for the grant or not. I thought each car can only receive the grant once but correct me if I'm wrong.
To go back to topic have a look here for a new 3pin charging lead way cheaper than the bmw one
https://www.amazon.co.uk/EV-Cables-PCD019-IEC-UK-10-Portable/dp/B01AGLK782/ref=pd_sbs_263_1?_encoding=UTF8&psc=1&refRID=7MNG182NGQXRGS9913V3
We all know and some of us have found to their surprise that if you hold the unlock button on the remote (accidently in your pocket) you find the car with the windows open.
I have had several cars with this option and to be honest in those 8 years used it twice maybe. So will i miss it...
What I do not understand is why BMW made the preheating of the battery only possible when plugged in. The consuption of the 1kW heater is very low compared to the cabin preheating which is possible without plugging in and can draw about 6kW. The 6kW heater costs you range but increases comfort...