Question

a leaving group such as H+ which departs without an electron pair is called an

Answer 1

Actually H⁺ is not considered as leaving group. It is known as proton and can be abstract by base in reaction.
Look at the definition of leaving group.
In substitution and elimination reaction, a group attached to the carbon atom breaks the bond with carbon and breaks away from the molecule with a pair of electrons and is called a leaving group.
A good leaving group should be able to break away from the molecule with the bonded pair of electrons and by itself should form a stable entity. An electronegative element bonded to a carbon chain is capable of pulling the bond pair electrons in a covalent bond towards itself and break away more easily. Hence H⁺ is not considered as leaving group.