I would really love for it to be explained, instead of just saying that's how it is. Like, Where did he get another keyblade or, how can he split WtD in half? As well as, why can't sora split his keyblades in half?
Sora can split his Keyblades in half, or did you just not use any Drive Form at all while playing KH2? He's dual-wielding there. One half gets to keep the original Keychain, and the other half gets a different one.
How come WtD changed to the one Kairi used when Riku gave half to Kairi, if that is indeed what he did?
Because, as far as we know, when you split a Keyblade, you can't split the Keychain.
Riku's half of the WtD kept the WtD keychain.
The half that Kairi took had a keychain forged from Riku's memories of Destiny Islands slapped on.
Has there ever been a theory about feelings for someone or the strength of a heart manifesting into a Keyblade, even temporarily?
I don't know if there's been a theory about that specifically, but I know there's been a theory about Ven's soul being in the KK.
It would maybe explain why Kairi was able to wield due to a possibility that in every heart is a keyblade, and the person whose heart it is can't summon it without help from an actual keyblade wielder or doesn't even know it's there. It's a little far-fetched, and isn't very thought out but still...
Kairi's able to wield because Riku said she could.
Just like how Riku was able to wield the Oblivion in his fight against Roxas. Roxas threw him the Keyblade, gave him permission to wield it, and it stayed. Until Roxas called it back.