First off: It's going to be a stunner.
Instead of sizing, you could use actual starch to stiffen up the white fabric. It does seem a bit thin.If you are not too far into the process, you could use a white that is equal to the thickness of the other fabrics. Otherwise, try starch.
It looks like your feed-dogs are pulling the pieces. You could tape a guide 1/4" from the center of the needle and then feed your fabric along the guide. Guides can be made from moleskin pads and some people use a pad of sticky notes. (The glue side facing the needle).
I still pin a lot - some people don't. If you don't pin, only sew about an inch at a time and make sure the layers are aligned at the edge. ALWAYS check the seam side to make sure the seam allowance didn't so something wonky. It is easier to rip and fix one small seam than notice an "off" seam in the top.
I wonder if your stitch length may be too short. Try using 2 or 2.5 mm with an 80-12 topstitch needle.
Also, go slow.
Pressing is another hot topic. I wonder if you could be over-pressing your blocks. Let the iron do the work for you by just pushing the top fabric back. Don't do the wiggely ironing motion.
That's about all I have to add. Good luck and have fun.