Kinda late to the party...but the first looks like clavicorona pyxidata. It's cestipose (grows on wood). While edible, ramaria formosa is a close look-alike - and is poisonous, causing digestive disturbances. If the flesh bruises and turns reddish-brown to black, it's the ramaria.

The second one looks like a coprinus or "inky cap." They get pretty big....

I had seen the ink cap as being similar, but I got to observe these over a period of a month, and they never (that I saw) dissolved into the inky goo that gives ink caps their name. They just shriveled up and died like (almost) any other mushroom.

I don't think the coral one was clavicorona pyxidata, because she is much more slender and can be very clearly seen growing on logs. This one is meaty, grows on soil (maybe buried wood) and looks more like one of appalachian ramarias, I eat them all. Cook well though. If you slice through the base of the coral and see some clear jelly contents, then it is the one blamed for upset stomachs. Never did me any harm again. Don't eat raw mushrooms. As to the coprinus-looking one, as long as it is really dark-spored, it still is a coprinus. I have seen them fail to turn into ink just because. Some coprinus species are tiny.