Well I guess if you look at it that way it would make sense to call Vanitas' heart a new one, after all he definitely is a new being.
That makes sense, it would definetly be in Vanitas' nature to do that, also as you said: according to Xehanort it was dangerous for Ven to be around Vanitas so he must have been draining him in some way.
I could actually see him doing something like that. It's really not hard to believe that while he was extracting the darkness from Ven's heart, he was implanting a piece of his own heart into the darkness to strengthen the being and to have a vessel for the backup Org if his plans failed.
That is the analogy, yes.
Xehanort also mentions the same behaviour when conferring with Terra about Vanitas and when he hints about why he would target Radiant Garden.
Exactly, and it would also serve as another backup for Xehanort in case Vanitas would try to betray him once he had the X-blade. As seen with Xigbar and Xemnas, the "Xehanort"-vessels are allowed to have a certain degree of personal individual freedom analog to how loyal they are to Xehanort, while the more rebellious or unwilling pawns would be controlled by Xehanort directly (like Terra).
As seen in BBS Vanitas also had a high degree of freedom, but Xehanort surely wouldn't be so stupid to risk Vanitas turning the X-blade (even if it's only a proto-blade) against him so he planted an emergency measure that would ensure that in the end he always has the upper hand if Vanitas decides to rebel.
In terms of Vanitas's heart during/after birth I like to think of it as having been "recast" and "reforged". Like when you take scraps of broken metal, melt them down, then make something new out of it. It's a collection of recycled materials but it's "new" none the less. When we see a ball of darkness encase Ven's heart fragment in the process of creating Vanitas (we even see him in fetal position for a moment for visual clarification that he's a "new born") not only is his body being constructed, I think that was also the "recasting and reforging" of the heart. The darkness that seemingly comes out of nowhere I think is what aided in stabilizing Vanitas's heart by functioning similarly to how Sora patched up Ven's heart only it was able to fill at least some of what wasn't there with raw darkness.
Also as Sephiroth said I think Xehanort may have aided in stabilizing him as well. Re-watching Vanitas's birth scene MX sends a dark beam into Ven before extracting his darkness.
I really like that explanation too, it also goes well with the notion that Xehanort "cut out" a part/shard of Ven's heart.
I also didn't even think of the analogy with the fetal position yet, good observation, makes full sense. That ball of darkness could then metaphysically even seen as Vanitas' "egg cell" from which he's born, with the "reforged" shard of Ven's heart as the core of his being where his own heart is then built around upon.
I'm inclined to believe Xehanort did the stabilizing with his heart, probably even a seed already like the others, in that case Vanitas' would be the "first seed".
As for the beam, wasn't that the attack from MX' Keyblade that cracked Ven's heart in two in the first place?
If I recall correctly MX shot that beam into his chest and Ven gasps while his eyes widen as his heart is ripped apart.
I guess that this very act is also the immense negativity that is created and later leads to the manifestation of the Unversed.