I'll see what I can do to help.
Well, Kingdom Hearts isn't really a single thing, it's a name that's just used to refer to anything that is a large gathering or container of Hearts. So yes, there are multiple ones depending on the kind of Heart they contain.
Uhm... Don't know what you're getting at here. There's a KH of Light and one of Dark, is that what you're trying to say? Because as far as we know there's no such thing.
Keep in mind that that one was merely a gathering of Hearts forced together, it's not a 'real' Kingdom Hearts like the one seen in the first game. In KH1, Kingdom Hearts, or at least the entrance to it, was a door, and inside it was all black piles and rocks etc. The appearance of a Kingdom Hearts most likely changes with the kind of Heart it contains.
Because Xehanort's Heartless is a being of Darkness, thus, Light has a damaging effect on it. Plus, Sora called on the Light of Kingdom Hearts at that point. Xemnas is a being of neither Light nor Dark, so they don't affect him in such a way, and Sora never really made any effort to call something out of KH like he did in the first game.
Like I said before, the KH in KH1 has always been there, it is the container of all the worlds' Hearts. The one in KH2 was merely a gathering of Hearts created by Organization XIII as a way to store more Hearts.