The melting point of a chemical solid is the temperature at which it turns from a solid to a liquid. It is a very commonly measured physical property used to determine purity and identity. In general, purer compounds have a smaller melting point range and less pure compounds have larger melting point ranges. Since the compound in question has a melting point range of 0.4 degrees C, it is a pure compound.
For part B of your question, it is not possible to identify an unknown substance based on melting point alone. There are many thousands of chemical solids so many different solids will have the same melting point. Melting point analysis is usually used to compare two different batches of the same compound and make sure that they match.