You pretty much named the 2 things you need to check, the timing belt and a tune. But of course you have oil and other fluid and filter changes, plus the turbo intake hose from the air filter tends to crack from flexing and heat, boost hoses are unpredictable, I am still running my OE ones. I hope you checked to see if your cooling system is getting pressurized from a bad head gasket? If you have any other concerns just ask I am sure someone here has seen or heard it before, just ask.
And welcome to your ownership of a unique vehicle.
