No that is not a cross, it is a ketoh design. We have a whole thread on these which you might be interested in.The Ketoh: Beauty in utility
And here is a very interesting video on the Twin Rocks Trading Post YouTube channel that discusses the design of it. This is a very highly regarded Trading Post in Bluff, UT, and they work very closely with their Navajo artists.
Beautiful buckle! I don’t really have a guess on the turquoise. Maybe you can contact him and see if he remembers, if he’s got an online presence; I know they sell a lot of his work at Twin Rocks so maybe they would have a way of getting a hold of him.