Generally for class black or white slippers are for the male students. Girls wear ballet pink slippers In class. The fact that you are a beginner and that a skirt is not part of standard attire as it is only used in for advanced students en pointe in variations or pas de deux classes I doubt that it will matter much. What matters more is the composition of the slippers. For a beginner they should be full sole leather and not split dole canvas. That being said you should contact your school to see if what you got is acceptable.
Regarding classes…. ballet has lots of repetition. Pay attention and incorporate all the corrections that your teacher gives you. Arrive early to warm up and strtetch. Let your teacher know about your healing hamstring. Stretch at the end of class as well when your body is warm. It helps prevent injury as well as increases your flexibility.