I also doubt turquoise. The second piece looks a bit similar to some variscite I have (definitely from Utah, I seem to recall Amatrice Hill area):
(https://s18.postimg.org/xdmm6amnt/2018march_variscite_utah00.jpg)
Difficult to know from photos these days, with so much dyed stuff (limestone and sometimes not even rock) coming in from China.
Quite a bit of variation in Amatrice Hill, however (as is the case with Clay Canyon). The piece in my previous post only has a bit of the blue-green variscite near the black webbing. Not all were the deep greens, and in the older finds they were looking for the translucent "Jade" type and robin's egg blues (Tiffany bought up a lot of this) that could be cut with little or no matrix showing. These also all came from Amatrice Hill:
(https://s18.postimg.org/p73t6a3nt/2018march_variscite_utah01.jpg)
Aside from "Jade" and robin's egg, there was "Apple Blossom" (opaque white on green), "Cobweb" (fractured and healed), "Green web" (fractures healed with dark green variscite) and some more complex material mixed with colored agate. Interesting to know what happened to the mine.