First off, while people have asked us if they are natural, I think that's not a very useful word to use. I have no idea what an artifical twin would be. They are however, spontaneous.
In terms of the question of monozygotic, aka identical, or dizygotic, aka fraternal, the answer currently is we don't really know. They each have their own placenta, but this is true for 30% of monozygotic twins as well as all fraternal twins. However, since eggplant has measured slightly smaller than heart on every single scan, my thought is they are likely dizygotic.
The shorthand summary I've worked out of mono vs. di is:
If they are in the same sac, they are identical. If they are boy/girl, they are fraternal. Everything else could go either way though there may be indicators towards one type or the other. Also, if they have different blood types, they are fraternal, but this won't be known until after they are born. The true gold standard to test is a zygosity test.