Temp warning and error code 2E84

[CarbonSchwarz125i]

Hi folks, as title states I have some issues with my car. Initially the orange temp light came on and then it went red with a large loss of power and I had to pull over. Fan was running quite loudly, observed low coolant levels however no evidence visibly of a leak anywhere so I checked the cap, no milkshake and no smoke of any kind in exhaust.

Decided to top off the low coolant with water as that's literally all I had to hand, did the procedure with the interior fan set to max heat, foot on throttle and nothing happened so I scanned the car and got error code 2E84 (image attached). I decided to limp it back and the temp light popped up again and disappeared twice during the 8 min trip, fan was running extremely loudly to the point people were looking at me.

Other observations I have is that my battery could easily be bad, the stop start feature as well as the automatic lights and wipers have never worked although I had the battery registered to the car when I purchased it and I've always had trouble with the drivers window unless I'm flooring it and then it will close fine.

I'm worried it could be a bad alternator or water pump, as those are pretty expensive fixes any advice would be welcome.