Cute cake! The fondant will dry from the air. I don't know of any way to avoid this.
First, your cake is beautiful. I think your accents may have been a bit thick. If you made these with fondant alone, its not going to dry very hard.
Even if the fondant pieces are not dried very hard. You cannot cut through them. They will fall from the cake............unless you cut around them.
You would need to use a serated knife and kinda saw through the slices so that it cuts the decos rather than pushing them down. Does that make sense?