A very easy way to improve your writing would be to separate your text into paragraphs. It doesn't take any intelligence but just awareness of norms.

It seems that my mind lights up with too many questions when I learn math, many of which are difficult to answer. (My professor does not have much time to meet students for consultations and I don't think I want to waste his time).

Math.stackexchange exists for that purpose.

Not everybody is good at math. That's okay. Scott Alexander who's an influential person in this community writes on his blog:

In Math, I just barely by the skin of my teeth scraped together a pass in Calculus with a C-. [...]“Scott Alexander, who by making a herculean effort managed to pass Calculus I, even though they kept throwing random things after the little curly S sign and pretending it made sense.”[...]I don’t want to have to accept the blame for being a lazy person who just didn’t try hard enough in Math.

Things such as why dividing by zero doesn't work confuses me and I often wonder at things such as the Fundamental Theorem of Calculus.

Math is about abstract thinking. That means "common sense" often doesn't work. One has to let go of naive assumptions and accept answers that don't seem obvious.

In many cases the ability to trust that established mathematical finding are correct even if you can't follow the proof that establishes them is an useful ability. It makes life easier.

In addition to what CCC wrote http://math.stackexchange.com/questions/26445/division-by-0 is a good explanation of the case.