Where exactly is the one seen in KH1 located? I assume it's smack dab between the realm of light and darkness, but I'm not sure?
It's accessed by way of the Realm of Darkness. "Where exactly" isn't really a proper question, because the "true" Kingdom Hearts isn't necessarily a corporeal essence, so its location isn't likely fixed or even relevant.
If the Door to Darkness leads to KH from the Realm of Light, is it safe to assume the Door to Light does the same from the Realm of Darkness?
Possibly, but not likely. Kingdom Hearts being located in the Realm of Darkness is representative of the light within the deepest darkness. The only way Kingdom Hearts in the form of KH1 can be accessed, anyhow, is by using the seven Princesses of Heart (i.e. pure light) to open the Door to Darkness.
If the DtD is right next to KH, what's stopping the Heartless from taking it?
Kingdom Hearts is pure light. It destroyed Ansem SoD, the strongest Heartless ever to exist (to our knowledge); any Heartless that attempted to corrupt it, presuming they could even sense it, would be instantly eradicated. Furthermore, the Heartless have no means by which to access or have any interest in Kingdom Hearts; Heartless simply function as manifestations of darkness, so they work entirely on instinct-- they aren't seeking Kingdom Hearts actively, although they are drawn to the Keyblade. Again, Ansem SoD was only even able to tap into it for a moment because he had already fulfilled other necessary requirements; the fact that it isn't there when Sora and Riku and Mickey close the DtD is further evidence that it isn't a physical
thing, it's a symbolic feature constituted of the power and energy of all Hearts. It's not meant to be claimed or owned by anyone, and likely never will be in that form. Therefore, the DtD is not "right next to" Kingdom Hearts: Kingdom Hearts is deep within the Realm of Darkness and its light shone from everywhere within it and out into the Abyss in order to destroy Ansem SoD once and for all. Or so it would seem.
-Why was the keyhole in Hollow Bastion significant in this regard? I always guessed because it was the keyhole that caused the barriers between worlds to collapse, but I'm not sure on that...
It's not clear what kind of Keyhole we saw in Hollow Bastion. The large one which Sora goes through would seem to lead to the true keyhole of Hollow Bastion (which is the one Sora locks with his Keyblade in the trippy rainbow room). That large Keyhole itself may have been artificial, constructed by Ansem SoD (or Apprentice Xehanort, possibly) around the true Keyhole in order to tap into its power in some way utilizing the Princesses of Heart (perhaps this is how he created a Keyblade from their Hearts).
-How exactly do Sora, Donald, Goofy and Ansem SoD reach KH from the End of the World then?
It's really only Ansem SoD who is able to summon Kingdom Hearts, but it isn't in any way clear (or really important) what he did. Kingdom Hearts itself may have responded to his beckoning in the same way the Door to Light in KH2 appears to Sora because his Heart called out to it (essentially). The point is, Ansem SoD needed to be able to unlock the Door to Darkness, which he succeeded in doing. From there, it seems he was able to call to Kingdom Hearts itself.
Finally, what is the difference between the KH summoned by the X-Blade and the KH seen in KH1? The former is said to be the "true" KH, but why is this? What purpose does KH1's hold?
The Kingdom Hearts summoned by Master Xehanort using the X-Blade is just another form of Kingdom Hearts. Nomura once said something to the effect of it being constituted of the "Hearts of all worlds" as opposed to Xemnas's, which is a Kingdom Hearts of the "Hearts of people," whereas the Kingdom Hearts in KH1 is simply a "true" Kingdom Hearts, essentially the life force of everything with no inherent physical presence. However, I think it's safe to say that the Kingdom Hearts which Master Xehanort sought was a form of it which could be more easily "obtained" and its power more easily "accessed." That's why a great war was fought in order to create the X-Blade and summon this Kingdom Hearts, rather than seeking the unobtainable manifestation of it which exists within the Realm of Darkness.
The important thing to remember is that Kingdom Hearts is more of a thematic factor in the KH series than a literal object or place. While it does have its role within the story, it's meant to represent great power as the Heart of everything. The best way to think of it is simply as being unfixed and all-encompassing. Kingdom Hearts doesn't follow any rules; everything we know about it is essentially speculation. In KH2, Ansem the Wise and Xemnas have a fantastic dialogue about the nature of the Heart and how it simply can not be understood by intellectual means (as evidenced by Ansem's failure to encode it into data). Xemnas's failed artificial Kingdom Hearts is, in my mind, representative of what happens when humans try to identify (and thus, limit to their own understanding) a force as ambivalent and ultimate as Kingdom Hearts itself. It might not be satisfying to some people, but I think, in the end, we just have to accept that there are no real, hard and fast answers as to the nature of Kingdom Hearts-- it isn't meant to be entirely comprehensible.