Negative of です can always be ではありません. But here you have to be careful because the notion of "negative" is quite different from what it is in latin-based languages. Like you could ask "what's the negative form of X in German/French/Italian" and you could get some usable information in real life from the answer you might get, but that's not guaranteed in Japanese. So I strongly caution against asking that question in the first place, if your goal was to add to your conversational repertoire. That's a rabbit hole you don't want to go down, beacuase people avoid the gramatically simple negative form like plague and hence there are numerious ways around it instead. Imagine if you will, a whole race of people avoiding "no"!
That said, you can say:
The gramatically simple, correct negative to it is:
...but you could cause some drama you don't intend to, depending on the context and who's around and what the subject it, saying that. Consider:
そうとは限りません。"that's not always the case".
As for negatives for ます、it's somewhat simpler. It's always ません。
As for turning
"I do not study because I am not a student":
First, omit the subject because it's obvious. (don't state the subject like I unless you really, really have to. By deafult, don't.) Now you have:
..and them, to answer your original question: