GCF and LCM will be most useful in algebra, but can be used in one fashion or another in all areas of mathematics.
Of course not, mathematics is a very useful ability for future careers.
Mathematics is one of the fundamental parts of knowledge. Just like being able to read and write. To not know how to do mathematics would be like not being able to read and would put you at a big disadvantage in a lot of areas of life.
IT is a wide area, so there are lots of areas where a need for mathematics is no so important. The reason for it being important is more for being able to deal with problems and think in a clear and logical way, rather than to do calculations. A computer will do a lot of the calculations for you. You may need to work out what calculations are needed, but not to do the actual calculations. A lot of mathematics covers other areas which make you think and try to work out different problems, often complex ones. The ability to think in a way to do that is what is important in some areas of computing, like programming. So it depends on what areas of IT you are going into. It is better to be good at mathematics, but not essential.
There are many possible titles of thesis' for mathematics. These titles will depend on the area of mathematics being studied.
Yes it does
No, but the children of mathematically able parents grow up in an environment where mathematics is not feared. There is no inverted snobbery about being poor at mathematics.
Yes, chemistry uses mathematics. But being great with mathematics is not enough for studying chemistry: you must enjoy the subject.
the number being multiplied
Engineering Mathematics
No. The suggestion that it does is absurd.
Statistics is one branch of mathematics being used in terrorist detection. Economics is another brand used to detect terrorist activities.
Archimedes' achievements in mathematics are some of the greatest ever made in the field, and include being the first person to mathematically calculate pi. He is considered to be the Father of Mathematics for this reason.