Hey Tindo, Nice shots! Looks like you had some fun.
In my neck of the woods, we have something that looks like the 'not a fungus' picture. Was it fragrant? Ours is called Indian Pipe as it is hollow, tubular, and has a nodding flower that looks much like the dissected picture. It's a saprophyte, using mycorrhizae associated with Pine root systems for food. So it has no chlorophyll! It is totally white and translucent.

It's really fragrant, kind of like blueberries! I usually smell it first, then start looking for it. Just thought maybe this info might help you nail down the ID. Sorry I'm not much help on the other one.