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For the first mushroom you don't state whether it is growing on the ground or on buried wood (habitat is very important in mushroom ID). Assuming it is growing on the ground it appears to be a Clitocybe, probably close to C. clavipes. Note that identification to species of all but a few Clitocybes is very difficult. If it is on buried wood the wavy gills suggest Hohenbuehelia, a genus split off from Pleurotus (the Oyster mushrooms). (A note for those who will be tempted to ask for a spore print - if you look closely at the plant stems closely alongside the mushrooms in the third photo you can see a deposit of white spores)
The second mushroom falls into a general group of wood inhabiting mushrooms called conks. I'm not that good at the conks, but looking at the older specimens (the ones you didn't photograph more closely below the pretty white one) I would guess Ganoderma. If the pore surface bruises brown readily (try writing on it with a twig) it is Ganoderma applanatum. Most conks are perennial, and you need to observe the older specimens along with the young, as well as section them to see the texture and color of the flesh to identify them accurately.