When you do a diamond quilt, you assemble the blocks on the diagonal (this is called a diagonal set) -- you do not need to fuss with seting in seams. They really go together pretty slick -- and yes the diamonds do nestle in together. If you are unsure, cut 9 diamonds out of paper (they don't have to be big) and put them together in 3 rows nestling the diamonds together. You cut triangles (or trim the diamonds on the edge flat if you want to avoid math) to make the edges straight. Just pick up your rows. I have some diamonds left over from a project in the sewing room -- if I can find them I will take pictures.
I usually starch them a lot because they are on the bias -- that way I keep the stretching to a minimum.