How can I know if I’m working through my PhD correctly?
My question is: how can I be know that I’m working through my PhD correctly?


Well, you can't as you haven't done it before, but in some sense you can never truly know anything, if that makes you feel better.  In any case, there's no "right way" to do a PhD.  Research is by nature a process where you wander into unknown territory, and at first you have no maps or guideposts.  Then maybe you find what you are looking for, and maybe you don't, but as some measure of reassurance:


After wandering around long enough, you can usually discover something new.  Many times it may just be a different point of view or minor results, but at least you have understood something new.  Still, usually when you spend a long time on a project you can get something publishable out of it in my experience.


Here are some other points regarding other things in your post:


Many PhD advisors are very hands-off.  It's also natural that they become less helpful as you go beyond the bounds of their expertise.  However, it's probably not great if your advisor is thinks what you're doing is uninteresting.  (I don't know if this is the case or not.)  It's probably worthwhile to have a meta-research talk with him, including whether he thinks it's worthwhile to continue along these lines or consider a different approach.
If you go out of the realm of your advisor's expertise, it might make sense to try talking to an expert who can give you better feedback.  Conferences are one good opportunity for this.
No professional mathematician has time to understand all or even most papers of interest to them.  You need to learn to prioritize, which it sounds like you're already doing.
You actually don't have to be that creative to do new things, or have too many new ideas, or be successful in research.  Many PhD theses boil down to learning a bunch of stuff and then doing computations.  This does not mean they are bad--many of them are very good.  It's also hard to be creative before you reach a certain level of understanding, so you may not realizes your creativity till later, at which point you will almost invariably think, "How did it take me so long to come up with that?  That's so simple."
Organizational skills are not so separate from creativity.  Many times problems can be understood easily after organizing your thoughts about them in the right way.  This was part of the Grothendieck philosophy, and I doubt many mathematicians criticized Grothendieck for not being creative enough.
While research can be frustrating and disheartening, you should generally enjoy learning and thinking about math, otherwise a PhD or academic track is not for you.  Most people have good times and hard times with research.  This is natural.  I view one of my most important duties as an advisor is to encourage my students to help them get through the hard times.