I think I can help with this one.
The blue thread is in step 1. If your design has unstitched areas, it helps to put in basting to create the outline of the stocking. This gives you a place to measure from when marking the line you will later cut along. In the tutorial, she used blue thread for creating this outline along the bottom of her project.
In step 7, you are basting through the two layers that make up the front of your stocking--the Aida (or other fabric) with your stitching and the lining you are using for the inside. One reason for this is that it keeps the two layers from slipping when you sew the stocking front to the back. The other reason is that once you put the front and back pieces together to do the seam around the edge, you will no longer be able to see the design. The design pointed inside, facing the right (outside) of the stocking back. If you have basted around the outline of the design, you can follow the basting lines while you sew the seam. This will also keep you from accidentally having a gap with unstitched fabric showing between the edge of you design and where the seam actually starts.
Hopefully someone else will weigh in about the batting. I've made a few stockings, but haven't used the batting. I'd imagine it would go between the outer layer and the lining layer, but I'd be afraid it would make the seam too bulky when you turned it right side out.
I hope this helps, and if it's not making sense, let me know. Sometimes things make sense in my head, but not so much once they land in the real world.