1.      Why does the temperature of a substance remain constant during its melting point or boiling point?

The temperature of a substance remains constant during melting and boiling points till the completion of melting and boiling because of latent heat of fusion used by the substances. Latent heat of fusion helps to overcome the force of attraction between particles of solid to change into liquid when they melt. Hence temperature remains constant.

I the same way during formation of vapours latent heat helps solid substance to convert into gaseous state. Hence temperature of a substance remain constant at boiling point.