Lengthwise/crosswise probably won't be a problem (meaning as long as it goes with the grain, which one it is does not matter). As to lining up at all, it depends on if they are lined up to give you plenty of stretch around the curve (needed) , or to give you the most stability along the finished straight edge (only needed if this is a problem area for you).
I also would not starch a curved edge before sewing, as you need it to stretch unless you plan on stay-stitching and clipping the seam allowance before you sew the curve. I find with only 1/4" allowance, I don't have to clip unless I'm doing a very tight curve. There is enough ease in the fabric as it is. However if a lot of the curve line ends up following a straight of grain, you'll have more problems getting it to set correctly.
I have the quick curve rulers, and they use the same cutting line for the pieces, so when you sew them, you actually are lining up a seam line that has slightly different radius curves. In that case, you really do need the stretch. If this pattern uses a method where you are cutting a block with a curve and swapping the inside/outside curves and sewing them together, you'll need the stretch and the lines will be more important as they as set to give you that ease needed for the curves. If you are getting templates for each piece so eh seam line matches up, it's less of a problem.