My answers are a bit different from Jonathan's.
1) She is the most successful student in my class. (Capitalize the first letter in the first word of a sentence)
2) I like exploring the library. ( You wouldn't use "in" unless you are referring to something in the library, not just the library. I like to explore *books* in the library. I like to explore *music* in the library.
3) She asked me a question about knitting techniques. (Same correction as your first sentence, capitalize the first letter)
4) This is a word I am trying to understand in English. (I think this what you want to say. Right now, your sentence doesn't make sense)
5) We are learning about weather in science class. (Doesn't need an "a". No need for an indefinite article, "in" not "at")
6) We are learning about weather at science class. (Perfect)
7) Knitting requires mathematical knowledge. ( "Need" doesn't work for your sentence. "Mathematics" doesn't fit in that tense).
Let me know if that helps or if you have more questions.