Sorcerer2006 wrote:
... but I believe that users should be able to manage their space by adjusting the size and selection of files they choose to store on their hard drive. And I believe they should have tools that can tell them how much available space they have without any hocus-pocus.
You can adjust the selection of files you store on the drive, but not the files that the system stores there, at least not without running the considerable risk of breaking something that can cause serious problems, up to & including data loss or the inability to boot the system normally. It is a very complex OS, with many processes that require considerable study just to understand what they do, much less how or why they do it. In fact, some processes are reserved for the exclusive use of the system's many non-human users, & provide services essential to the normal functioning of the machine.
You are provided with all the tools needed to see how much disk space is available for your use -- that's what the graphics display like in your screen shots shows you. The display is straightforward, explicitly indicating the space used by certain specific types of files & lumping everything else into the "Other" section. Since there are literally dozens of different types of files that are or can be stored in both the user & system domains, it isn't practical (or for some things possible) to break things down further than that. As has been mentioned several times, some directories simply cannot even be read by regular or admin users, or altered or executed by any user other than the one non-human user that provides some low level system service. This is a major part of the security model of Unix & Unix-like systems, & in El Capitan it has been extended even further with the addition of so-called "rootless" System Integrity Protection, which denies write access to some files even by root.
If it helps, you can think of "Other" as "Everything Else," but you won't ever be able to see everything that includes without altering the fundamental way the OS works, at which point you will be on your own, without the support of Apple & taking full responsibility for the consequences of doing so.
As for any problems you might be having with the existing OS, aside from not understanding what is using some of the disk space, what specific problems are you actually seeing? Is the system sluggish, unstable, or anything like that? Do you see frequent application crashes or other error messages in the normal use of your Mac? If not, the only real problem is basically what you might call an intellectual one, which is why there has been so much focus on that.
For that, I suggest you consider browsing through the enormous amount of developer documentation Apple makes available at https://developer.apple.com/resources/ & possibly enrolling in the developer program. (Both free & paid accounts are available). I know of no better way to get insights into the "how & why" of the many facets of OS X.