"Is there a way to export CorelDraw layers into Photo-Paint?"

No, since PhotoPaint doesn't do layers. However you can try these three alternatives:

1) Explore the bitmap effects available right within Draw. Convert one of your objects to a bitmap (Bitmap/ Convert to Bitmap) and then check out the long list of effects that can be applied from the Bitmap menu without leaving Draw.

2) Or use PhotoPaint, but use it from within Draw. Convert an object to a bitmap as above, and then right click on the item and select "Edit Bitmap". PhotoPaint will be launched and you can make changes. When you're done, close PhotoPaint and the revised image will be there in Draw.

3) Or, cut and paste (or drag and drop) the objects from Draw into PhotoPaint. They'll come into PhotoPaint as objects that you can reorder and otherwise manage using the Objects docker. The disadvantage of this third method (although it's the most Adobe-like alternative) is that all X-Y positioning is lost in going back and forth.