Sometimes I sew the "X", sometimes I don't, it does help to stabilize the fabric if you do though. I do normally use a contrasting flannel for the batting and cut it the same size of my other 2 squares and when it's washed, all the colors will fringe and look great!
Another tip that I've used for years and it works great and washes out when you launder it, after I cut all my squares, and I'm ready to put all my squares together, I get one of those glue sticks like you used to use in school and just put a dab in the middle of my bottom square and put my batting/flannel in the middle, another dab of the glue stick and put my top square on. This helps to just keep everything in place when you start sewing!
Good luck and have fun! I get on a rag purse kick and will knock out 4 - 5 a day!! They are so much fun!