Mathematics is the language of physics. You cannot do well in physics unless you can handle the math. If you are excellent at math, you have a better chance of being very good or excellent in physics, too.
Let's take just one example from your question: Physics. If you aren't excellent in math, you don't stand a chance in physics.
Physics and chemistry use mathematics in order to quantify their observations about the world. Most mathematics were invented by scientists who needed the math to quantify their work.
All of those topics are very heavy in math. If you have a good math background and are very good at math, these topics will be easier for you to understand them.
No, a person who is good at math will have the best chance of doing well in physics.
Because there are a lot of formulas that require a higher level of math to do them correctly
Of those six disciplines listed, you can possibly have "so-so" math skills and still make a good biologist. But an excellent facility with higher mathematics is a requisite for the other five areas.
It really depends. If you are good at understanding the concepts of math and you think you can grasp the concepts of physics (which is not bad at all), then you will do fine in physics. Physics is like 50% math 50% concepts. This is my second year of physics (I am doing Physics with Calculus now) and it really isn't as bad as most people think.
Generally the opposite is true as chemistry and physics are heavily mathematically based
Yes, it is true. It is also true that some peope who are excellent at math will have a hard time with tieing their shoes and with pole-vaulting. Generally, however, in the majority of cases, most people who are excellent at math will also be quite good with Physics and Chemistry, if they're interested in it and willing to put forth a modicum of effort.
No, that will definitely not be the cause. On the contrary, you need lots of math, especially in physics and engineering.
Yes. It is equally true that some people won't.
Not at at all, both fields are mathematics heavy.