Super handy extension. Unfortunately the extension warehouse is down for maintenance right now, should be back this evening, assuming you are in Texas.
Yes, it’s down for just a bit, although I believe it should have been back by now, but will be shortly I’m sure.
Yes it’ll stay a solid and you can put a hole through it, I would model it at x1000 size to be sure you have no tiny faces issues. Do you want this shape on both sides or just one side with a flat side on the other? If on both sides the resulting shape will be tricky to print and will need some supports, assuming you are 3D printing this.
Personally I like Tig’s Extrusion tools for this sort of thing. And Fredo’s bezier to shape the curve. In this rather clumsy gif I have exaggerated the curve for effect.
I imagine @box is sleeping right now, I’m sure he will be back on very soon with some more excellent tips. There are a few problems with this file you posted. The two halves do not meet up exactly, so there are holes in your mesh. There are also still tiny edges here, the model you posted is only 1.7 meters across. I would model it at 170m across, using meters as mm. At this point now that you have joined the two halves and exploded everything it’s going to be very tedious to fix, or even to take the halves apart again. If you want to print halves separately and glue them together there is no need to ever make a whole version.
Let’s back up a bit. Regardless of what method you use to make the heart geometry, start with the heart half, modeled at 1000x and work on making that solid.