Question

why does ice melt at zero degrees Celsius without an increase in temperature, even though heat is flowing from the surroundings into the system (the ice)

Answer 1

whatever energy is being added goes into breaking the bonds holding neighboring water molecules together, rather than increase the speed of the water molecules, which would increase their temp. Once all the bonds have been sufficiently loosened, the water will be entirely liquid, and the added energy can continue to heat up the water