Which of the following properties must be known in order to calculate the amount of heat needed to melt 1.0 kg of ice at 0ºC?
I. The specific heat of water
II. The latent heat of fusion for water
III. The density of water

If you're only melting ice ... turning solid ice at 0°C into liquid water at 0°C ...then you only need to know the latent heat of fusion for water.  That's exactly what it means ... the amount of energy involved when a gram of H₂O changes in either direction between liquid and solid, with no changein temperature.