1997 Other BMW Models cooling system puzzle - stumped

This is kind of a nightmare for me. In the last months my car has been in the shop 5 times and it is still not fixed. BMW 1997 540i, 167Kmiles,

Car overheated. Someone else driving - don’t know how long they drove it hot.

(1) First they repaired the cooling system (don’t remember what it was), but the thermostat which normally holds solid in the middle, varied when I
drove it, after the repair, high as ¾ warm, but not in the red. Thought it was OK.

(2) A few weeks later, a part broke off the radiator. Had it repaired?

(3) 3 or 4 weeks later car overheated again - changed thermostat and a hose torn from hitting against a fan belt. Thermostat works great now, solid in the middle. The guy tell me if it happens again it could be that the engine was damaged by the overheating and fixing the cooling system is useless because the pressure will build up in the engine and compromise the cooling system. They wanted to take the engine apart, big $$$. I am tired of these guys now, and thinking that there should be another way to check if the engine is damaged besides waiting for a 4th water leak.

(4) 3 weeks later, the water pump brakes. Took it to another shop. They tell me about the cascading cooling problem. Older cars are a little leaky, when you seal them up tight after a repair, they sometimes burst at the next weekest link because thy are not used to being so tight. OK. They fix the water pump and told me the cooling system was sealed up fine, but they said the car is running really rough and asked me to pay for a diagnostics. I did. It was the intake manifold. They fixed it and according to them the engine is running fine now.

(5) BUT when they did the diagnosis, the valley pan began to leak coolant and now they want to repair that, which is NOT CHEEP. $$$$1500 and I am already $$$$2000 into this cooling system.

How do I know if I get this valley pan fixed that something else will not brake in two or three weeks? Wouldn’t their diagnostics identify an engine problem from overheating? Could the first guy be right? Is the only way to tell if the engine is warped is to take it all apart? Is it right that if the engine was compromized that cascading cooling problems would occure.

Just don't know what to do here. I am thinking to take it back to the first guy and have him take it apart. I am a lady with no knowledge of these things. What would you do?