I use json.tool a lot to format JSON directly in vim. Simply highlight the text you want to format and run :!python3 -m json.tool. There are probably plugins to do this too, but doing it this way is probably the simplest, unless vim has a built-in for it.
Yeah, I knew someone was going to say that. Usually it's more likely that Python is installed than jq - especially on servers. But yes, that would definitely work too.
No. But, it does provide a list of all stdlib libraries and those, like gzip, that are intended to be compatible with the CLI tend to have explicit documentation showing usage (ex. https://docs.python.org/3/library/gzip.html) and provides any other contextual info related to using the library.
Don't get me wrong, grepping through the code is a great way of building skills needed as a professional. Really, I have to do this kind of thing multiple times every week at work. It is, however, also worth noting that Python only uses an "honor system" for public/private functions, methods, and classes so modules having an "if name == 'main'" block doesn't necessarily mean that they are appropriate to use as CLI tools. They might be but, without documentation to back it up, it's an "at your own risk" situation.