I don't worry about my fabric pieces running exactly on grain unless I am matching a plaid or stripe. Your quilt pieces will have little threads along the edge sometimes, just don't pull on them. When the seams are sewn the little thread ends won't matter. For your seams not laying flat, I find that Aurifil 50wt thread works the best for a nice flat seam. Are you using cotton fabric? Fabric with a bit of polyester in it will not lay as flat as cotton when ironed.