Though I can easily find an alphabetical list of all available formulae, there seems to be no resource online, including at Brew's Github, or seemingly anywhere where I'm able to browse through Homebrew formulae non-alphabetically, using other sort methods (# downloads all time, for example). Neither does any resource exist out there that provides categorizations of them (compiling tools, essential formulae, for fun, etc.). Is anyone aware of any resources that exist out there? Thanks in advance.
There are some vague or basic categorizations available under the "Alternative Repositories" section of http://braumeister.org/ - though certainly not nearly as comprehensive as what you're suggesting.
While certain categorization and sort methods you mention sound extremely useful, I have a feeling they are a quite challenging to implement in a very automated approach. Sounds like a great challenge for someone.