The element crystalline is brittle and has a high melting point, why does it have these properties?

Answer 1

You are describing a typical ionic salt.

Becuae it has a strong electrostatic atraction due to ionic bonding, it has the properties you describe.

High melting point becaue it is hard to pull the ionic molecules apart

Brittle because it forms a rigid crystal lattice, and so it will fracture rather than bend when hit hard.