No. The laws of thermodynamics were fully operational
long before anybody knew anything about math.
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.
If your also good at physics/science, then no.
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.
the ability to do math
a student's ability to reason using math
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.
There were several mathematical ideas which interacted with thermodynamics. By far the most important of these is statistics.Some physicists believe that the Second Law of Thermodynamics is the one physical law of whose validity we can be totally certain, because it is based on statistics.
It will depend from person to person. Some prefer music while solving math problems, but some cant stand it while working.
Dysgraphia
Math rules depend on what kins of problem you are doing.
For thermal energy, thermodynamics. For energy of movement, mechanics.