Is a jew allowed to learn secular studies and science? Is there a prohibition against learning any secular subjects and/or science?
Let me summarize it for you in one sentence:
It's not about what you learn, it is about why you learn it.
If you learn science to help you with the understanding of Halachic topics, or for observing Mitzvot, or for making your living - it is not only allowed but necessary and obligatory.
If you learn for to stray away from the Jewish tradition or things that will drag you from the path of the just - you are strictly forbidden to do so.