You should probably use one of the existing libraries. You can do a rudimentary API request in maybe six lines of code, but in practice you'll want error handling, logging, backoff when the servers are overloaded etc. which is a lot of boilerplate that existing libraries will handle for you. See https://www.mediawiki.org/wiki/API:Client_code#Python

Yeah, it's the recommended method as it frees you from having to deal with login at all.