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.
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.
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.
If your also good at physics/science, then no.
Possibly. You also have to be good at and enjoy engineering concepts which do involve math.
You'll certainly not fail physics BECAUSE you are good at math - you NEED math for physics and engineering.
Thermodynamics is a part of physics, and physics is very closely related to maths. Physics involves a lot of mathematical equations and problems, and as such, to be good in thermodynamics, you have to be good in maths.
No, this is not obligatory.
You need good math to do engineering at a professional level.