Is a graphing calculator a necessity when one studies a higher level of maths? Is it required, and what are the main uses and advantages/disadvantages that come with them?
 A: The answer depends on what you mean by "higher level of maths".  Back when I was in middle and high school, I thought (very incorrectly) that the highest "level" of math was calculus.  If this is all you're talking about, then a graphing calculator is certainly not necessary, but it can be very useful. Being able to immediately graph and see a function to get idea of what you should be getting for the integral/ derivative of a function is invaluable.  However, keep in mind that most university professors don't allow students to use a graphing calculator on exams.
If by "higher level of maths" you mean, say graduate school level math, then the answer is most certainly no.  For, as Mark points out in his answer, most math at this level doesn't even involve calculating numbers or dealing with elementary functions from $\Bbb R \to \Bbb R$.
A: Definitely not necessary.  99% of "higher" math has nothing to do with calculating numbers or graphing functions.  And for the tiny bit that does, understanding functions by graphing them by hand (using all the tricks that makes this easier) is probably just as useful as just looking at the curve on your calculator screen.
