Hello! The puzzle pieces both require the pickaxe pencil, and the second requires the egg pencil as well. The first is just below the player starting point behind some rocks inside a cave. The other is at the very end of the level. Instead of grabbing the pages, draw an egg in the nest on the mountain, bust through the rocks to the left and grab the feather. The bird will pick you up and you'll get the puzzle piece as he takes you to the top of the mountain.
I'm sorry, but I'm not sure what you mean by the river. As far as I know, there's no puzzle that requires filling anything with water in level 1!