No.
Success at math is more likely to improve your skills at thermodynamics. All sciences benefit from some degree of math skill even if only for the ability to think in logical terms.
Any generalisation of that kind is total nonsense.
Mathematics is an important part of all the other sciences such as chemistry and thermodynamics; mathematics has rightly been called the language of science. So no, being good at math does not mean that you will fail chemistry, quite the opposite.
The opposite is true. You will more than likely be good at science.
No, this is a generalization and a stereotype. Most sciences require mathematics to function, and statements like this are fallacies and myths.
no
No, this is not obligatory.
No.
You need good math to do engineering at a professional level.
You'll certainly not fail physics BECAUSE you are good at math - you NEED math for physics and engineering.
No, it is not true. It is false.
I'm good at Math and I passed Chemistry.
No, it is a myth.