"Double Back Stitch" -- This may be the same stitch that was used on the items that I pinned made in Mexico in the "traditional Mazahua" style or method. (This looks like it might be more complicated and more dense though.
This is an easy pattern. Circles are easy to crochet in general in simple dc, sc, etc.: just keep increasing groupings one more stitch farther apart for each and every new row and the circle should lay flat even if you keep going like that for forever.