(a) Diamond is one of the hardest substance which occurs naturally.
The atoms in diamond are organised in a rigid three-dimensional structure and are tightly bonded to each other. The absence of large empty spaces in the diamond structure makes it an extremely hard substance which compels it to use as cutting tools such as glass cutter while graphite is a layered structure of carbon atoms and is very soft so, it cannot be used for making cutting tools.
(b) In a graphite molecule, one valence electron of each carbon atom remains free in its two dimensional structure.
Due to the free electrons in its framework, graphite act as a good conductor of electricity. While in case of diamond, they have no free mobile electron in its rigid three dimensional structure hence cannot perform electrical conductance through it.
Therefore, graphite can be used to make elctrodes in dry cells but diamond cannot.