When you put a sealed bottle of water in the freezer it explodes, (I get this part). I was told that filling it with 100% water (removing the air) first stops the bottle from exploding as this allows the water to expand more. Is this true? If so, why?
You want some air space. Air is very compressible, but water is not. Pulling a vacuum to remove all the air and leave a headspace in a "vacuum" (will still have vapor pressure of water...) above the water requires a container that can handle a vacuum.
Water expands on freezing so it the container is absolutely full of water then the container must either stretch or burst.
I dont think this is true. If you were able to extract the air from a bottle you would form a vacuum inside the bottle, which will make the water inside to boil until it fills the vacuum with water vapor (until the vapor pressure reaches equilibrium), so you should end with roughly the same volume of solid ice.