Kairi however is not that easy to explain.....well at least since SquarEnix has yet to do so lol.
They did. And like 99% of the plot of KH2, they did so in the novels.
I believe that Kairi can wield a keyblade because through almost all of KH1 her heart was inside of Sora's.
That's why we're calling it smooching.
Namine though would make a better explanation, seeing how if Roxas got Sora's Wielding abilities, one can argue Namine did too, in a way, also being a Nobody born of Sora.
Then Kairi got the abilities once Namine faded after they met with Riku - Namine disappeared until later, after all, and she appeared faded then, which makes one believe she was already inside Kairi, only to reappear when she was needed.
The most likely explanation is a combination of Kairi being a PoH, thus making her related to the Keyblades, and Riku willingly letting her hold it, much like Roxas let Riku wield the Oblivion when they fought.
As for the keyblade itself.....well it has an islandy feel to it. So I think it might represent Destiny Island in some way.
You are correct sir.
Meeting Kairi again made Riku remember Home - being Destiny Islands. Thus the beach plot and the waves, the vines, the flowers, and above all else, the one thing to represent Destiny Islands the best - the Paopu fruit on the Keychain.
Kairi being the one to make Riku remember it all is why the Keyblade is so pink, seeing how in a way it's based on her, much like Sora's Oathkeeper is based on Kairi and Namine, thus bearing resemblance to Namine in design.