Price wise yes you have paid over the top since you went to BMW. The battery and tyres would have cost you way less if you went elsewhere. The 19" wheels are prone to cracking and many have had them repaired. Some say repaired cracked wheels if done correctly are fine and others say they are not including your BMW dealer.
But clearly the MOT station thought they were within the legal boundaries and main dealers are known for playing up severity of faults designed to get you to part with your cash. I was once told by a Ford dealership my rear brakes pad were shot and needed immediate replacement. Well it turns out I did not actually replace them until a 1.5 to 2 years later!
Why the tyres were not picked up in the MOT is a question though. Maybe BMW meant borderline thread at 3mm because they generally change them at 3mm whereas the legal limit is 1.6mm and therefore it would have passed the MOT? I don't really know and it could be argued that the deep cut could have been picked up in the 300 miles or so that you drove it and wasn't there at the time you purchased it.
Dealers have a duty to tell you if the car has had any major accident repairs although I am not sure if this also means repaired / refurbished wheels but either way I would contact the dealer that sold the car and advise them of the tyres and repaired wheels.
But clearly the MOT station thought they were within the legal boundaries and main dealers are known for playing up severity of faults designed to get you to part with your cash. I was once told by a Ford dealership my rear brakes pad were shot and needed immediate replacement. Well it turns out I did not actually replace them until a 1.5 to 2 years later!
Why the tyres were not picked up in the MOT is a question though. Maybe BMW meant borderline thread at 3mm because they generally change them at 3mm whereas the legal limit is 1.6mm and therefore it would have passed the MOT? I don't really know and it could be argued that the deep cut could have been picked up in the 300 miles or so that you drove it and wasn't there at the time you purchased it.
Dealers have a duty to tell you if the car has had any major accident repairs although I am not sure if this also means repaired / refurbished wheels but either way I would contact the dealer that sold the car and advise them of the tyres and repaired wheels.