How to translate these inspirational phrases correctly?
If you can dream it you can do it!
  梦得到的都做得到！ (what can be dreamed of can be done!)


梦得到的 that which can be dreamed (the 的 changes 梦得到 "can be dreamed" to "that which can be dreamed")
都 all (adverb)
做得到 can be done

verb得到 means "able to successfully verb". The opposite is verb不到. This is called the "potential complement" and is a common grammar pattern.


  You're the number one student!
  你是最佳学生！


你
是 are
最佳学生 best student (最佳X is a commmon pattern meaning best X, often used for best player in a football team etc)


  Best of luck in Mathematics and Science!


This one's a bit trickier. Do you mean "best of luck in the Mathematics and Science exam"? (or are they two different courses?). Or do you mean good luck with the course in general, not specifically the exam?