Question

why in solid conductors negatively charged electrons conduct and positive ions are fixed

Answer 1

Both the negative and positive charges have an important role in the conduction of electricity. These are not static and can move. Positive charges move more slowly than electrons. When electrons move in one direction, these positive charges move in the opposite direction. In solid conductors it is basically the flow of electrons that constitute current. However, the direction of current is opposite to the direction of flow of electrons. In a gaseous or liquid substance the flow of positive and negative ions constitute current. The direction of positive ions (not protons) is same as the direction of current.
In solid conductors, postive charges i.e. protons don’t take part in conduction since they are fixed within the nucleus of an atom. These charges can't be easily removed from the nucleus for the conduction.