Oh shoot, I always forget about this. It is actually Sora`s body walking around, with the appearance of Ventus. For a few years I had thought that a separate body had been made, but this is not the case. This blew my mind when I realized a few years ago.
Hmm, and of course like other have said, the similar state in which Kairi was in KH1 could really well represent the outcome. Dang it, how I did not think of that.
If you want to be 100% nitpicky about it, yes, it is Sora's
old/original body that gets hauled around by Roxas, shaped to look like Ventus (except the eyebrows, as these remain brown).
The games themselves do not really help with the issue though as after Kairi restored Sora back from being a Heartless, Sora clearly had a physical vessel/body as well as Roxas did at the same time.
Whatever that "vessel" is/was (some fans coined the term PPS = Projected Physical Shell), it certainly functioned apparently just the same as Sora's old body and reacted to things (like i.e. getting kicked by Larxene) just like any normal body would.
It is simply unknown by all available means what exactly this new vessel of Sora is/was, it might indeed be a new, separate body or something else.
For the issue with Ven's heart though it is imperative to keep in mind that
Sora is the one with a new physical vessel (whatever it is) after Kairi restores him, his old body is Roxas and that's where Ven's heart is.
That's the case for the time of KH 1, yes.
Now if one wants to theorize and contemplate "what ifs" a bit more, maybe one should look at the fact that while Kairi's heart entered Sora during the events of KH 1 itself, Ven's heart had been there since Sora was four years old, meaning for ten years. If it had been always active and healthy, Sora would probably have had contact with it much earlier during his childhood.
Of course, strictly spoken if Ven's heart
truly had been active and healthy it probably would still be in its own body and not inside Sora at all.
After all, the fact that the heart was so badly wounded was the driving point behind the whole issue in the first place.
Sora felt the pain through the already forged connection between them and on Riku's suggestion called out which eventually led Ven's heart there.
Kairi's heart sought Sora out because he was the nearest heart in the vicinity at the crucial moment as it was in danger and seeked protection, Ven's heart however was proactively contacted by kid-Sora across world-borders and provided a resting place.