Your example is perfect. Note that “take advantage of” can also have a different and negative connotation. The shopkeeper took advantage of my ignorance and overcharged me. He takes advantage of his wife. He’s getting away with it now but it will lead to problems in the future, I predict. This negative use can also be written as “takes an unfair advantage”

Yes its correct to say that in this context.

Yes, you can say that. As Michael suggested, another expression with the same meaning is, "I used my free days to study". By the way, your use of 'free days' is fine where I am.

Perfect. Thank you all of you guys.

Depending on your exact meaning, you could also say, "I had a light week so I was able to study."