you are making flying geese with folded squares. no triangles to deal with. those are dimensional.
you lay them on the upper corners with the center tips over lapping, then stitching them down 1/8 from top edge. i would think you could also stitch them down on the sides with 1/8 seam too. then you have flying geese that wont' slip or come apart.
yes, the sqs will stay folded and form the flying geese. the fold never gets stitched unless you want to do so when quilting the whole quilt.
should make great quilt blocks. so yes, stitch them down the sides too and all will be well.