You can do they(paper piece) technique by hand, Ginny Beyer makes all of her quilts by hand. You can either USA a foundation (I use muslin generally) or you can use templates. Yes, the piecing order is correct in your diagram, you piece your spike section first, I would join sections 3 & 4 then add that section to the spike section, then add your corner piece. That is the order New York beauty blocks are constructed