Let me respond to this in two parts:
1. First of all, I think it's generally true that mathematical knowledge and skill is related to the ability to write and test code successfully. The mathematics that many or most programmers need includes graph theory, linear algebra, set theory, algorithm theory, and various other areas of mathematics and computer science that some people might not include in the term 'mathematics'.
2. Being a successful programmer also involves mastering a lot of other skills, especially in communication.
I worked in computing and software for decades myself. I've added a URL which outlines some of the other stuff that's involved in the occupation.
I think so because my brother in law is computer scientist and he says that if you are good at mathematics so programming will be easy to learn for you.
Yes. An understanding of mathematics is essential for an understanding of computers.
No, you probably won't fail computer science. Probably. Mathematics involves logic and problem solving - which is a major part of computer science. Although programming is also a big part of computer science, there are quite a lot of branches to do with computers, and you don't necessarily have to work with programming. I'm good at maths and not so good at programming but I still did pretty well (better than all the hard-core programmers) in the computer science / programming class. If that's any consolation.
Not true. Chemistry is easier than Mathematics.
No.
No
No, it is not true. It is false. In order to PASS physics, chemistry, and engineering, you must be pretty good at mathematics.
It depends.
Not you will but you can.
No.
This is not necessarily true. It depends on how good you are a programming rather then speaking languages. It may be that people who come from different countries speak the language of where they come from and decide to do programming as their job.
The statement seems absurd to me.