Xion probably had a heart of her own, if we assume her composition was the same as Riku's Replica, who attested well enough to having a Heart of his own and mocked the CoM Org members about it.
However, as you said, her Keyblade was an imitation of one, and her "qualification" to wield - copied to stolen from Roxas.
I doubt that's why they wanted Hearts, but time will tell. As for Xemnas not being able to wield, then we have two factors to consider about why he had no Keyblade, despite obviously being related to at least one out of Terra, MX and maybe even DS.
1) Xehanort the Apprentice lost his Memories. Therefore, even if he was a qualified wielder, he would still be unable to wield, going by KH2's Roxas before he underwent his Destati and rediscovered his Keyblade.
2) Roxas has the Ven factor going for him which would let him wield at the same time Sora did. However, nothing guarantees that Xemnas would enjoy something like that. Namely - XH would've had the Keyblade neither of them could reach until arguably Riku Duel Wielded thanks to him, leaving Xemnas without access to it.
As for Saix... I personally don't believe his Somebody relates to anyone we know. Least of all Terra. But then again I'm not up to date with BBS news so, meh.
My 2 cents on the matter.