floating shelves are typically installed one of two ways:
solid core shelves: using a metal plate with two (or more) fingers that protrude and insert into the shelf. the plate is screwed to the wall and then the shelf slides over the fingers - no hardware is visible. usually there is a little screw on the top of the shelf that secures the shelf against the finger (like you secure a towel rod to the bracket on the wall)
hollow core shelve: use a wooden cleat - attach it to the wall and then slide the shelf (its hollow and open on the back side) over it and secure it with screws from the top of the shelf, into the cleat.

toilet up off the floor is a good idea. dont want a wooden and tile mixture for sin, but i do like the fixtures being in the wall I think

super helpful on how to float the shelves! Where did you find these shelves?