If you want to use braid or cord that will have raw edges, they should go in as you piece the block so you can sew over the raw edges with the next piece. Fancy stitches can be sewn on finished blocks either by hand or machine however, depending on what you are using for your background, you might want to remove the paper before machine sewing the fancy stitches as the paper may not come off well.
You can use your fancy stitches to quilt but you would have to keep the machine stitching fairly open because you will be quilting through a lot of layers.