The first one is indeed a saprophyte (my grandmother would say "Look it up, you'll remember it longer") most commonly known as Indian Pipe. The 'pipe' shape is obvious when they're young, and when they get to the point of releasing spores they straighten up and the inside of the 'bowl' of the pipe looks red.
The second one is probably an Amanita; they're sometimes known as Agarics. There are a lot of different species, and my ID books are all in storage at the moment. Best rule of thumb for mushrooms is, if you don't ABSOLUTELY know it, leave it alone. "I saw a squirrel eating one" definitely does not work.