I want to know what these are? ?

My mom just went to Manzanillo Mexico and I know Mexico has 60+ different minerals they have an mine there so I asked her to grab me anything she could find, seeing I'm an avid crystal, rock hound. She came back with some onyx, jade necklace, and 2 that I cannot figure out what they are. My question is, what are these 2 specimens? They ARE NOT died and were bought in Mexico from a shop that had many many different minerals, she said the man named the blue stone but she cannot remember what he said. Greatly appreciate an answer. I thought the purple one possibly fire opal or my friend thought tanzanite. Hope to hear back with an answer.