Axel said Roxas made him feel like he had a Heart, so that might explain the tear even. Being next to someone that brought about the Memories of his emotions in an intense manner would make him go the distance and even cry, and then kill himself to protect said person.
I really doubt he has a Heart though.
As for Xion and Roxas, I'd sooner say Xion has one before Roxas does, but that's because we know all but nothing about her, even less than about Roxas.
As for Roxas, I'd sooner explain him having anything of Ven's in him that is not a Heart. Even Memories of Ven's emotions would explain Roxas seemingly having a Heart, seeing how he'd have something he wasn't supposed to have. Added Memories or Sense of Self, making him receive some from two people instead of one would very much stand to explain how come his game of "pretend" seems to be the best aside from maybe Naminé thus far.