Testing APIs is potentially endless, just like almost anything in testing. I recommend focusing on one area rather than drowning yourself in something completely new. That would be a recipe for failure.
If you're completely new to the world of APIs, I recommend installing Postman (or any other client) and playing around with some endpoints for a bit. No need to start looking for any bugs yet, you need to learn what endpoints mean, how to interact with them etc. It won't hurt you if you read something about HTTP protocol, since you need to know (sooner or later) that as well.
Having said that, you can focus on many different things when testing APIs, a good starting point could be found here.
Then you asked specifically about Python. I don't know what your experience with the language is, but you need to know at least some basics before jumping in to create an automation suite for that API of yours. What I've used throughout some of the projects I've worked on is a combination of Python, pytest, and of course requests library for actually sending requests to the API. You'd probably need to read pytest documentation and search for further examples as you go.
Regarding PyCharm. That's a concrete tool you can use for typing your code in. I don't think this is important to discuss in this context. Different people use different IDEs, what matters is how well you can handle your tools. If you are efficient in PyCharm, fine, use it, if not, you can choose something else like VSCode.