The engine will stall if you remove the oil cap as it is losing crankcase pressure and creating an air leak that should normally be recirculated into the intake, that is why the engine will stall or turn off.
As for the cooling system, I thought it could be blown head gasket causing more pressure in the system causing the hoses to blow off, but you said that it has no signs of a BHG, probably something clogged that is restricting flow, causing the hose to blow off.
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