Mushroom

The resupinate sheet fungi with the wavy margin would be the saprobic one and the white fur?, without a macro view, might be some Hypomyces sp. - http://www.mushroomexpert.com/hypomyces.html or even a parasitic pin mold like Spinella sp. https://en.wikipedia.org/wiki/Spinellus but we would need to see it very closely indeed. Here's my pin mold spotting http://www.projectnoah.org/spottings/11944172 and here's a Hypomyces http://www.projectnoah.org/spottings/25577035 There are probably many more options for fungi on fungi parasitism.

This one is really interesting. A toothed shelf fungi on the timber (which really focuses ID options) and another white 'parasitic' mold type fungi which seems to be growing on the first one.