1. I don't remember from school but I found
here that Volta pile was simply a series of copper and zinc discs separated by piece of cloth soaked in brine. A very primitive and inefficient setup, although it looked as Volta knew to connect the cells in series to add the electric potentials. Today's batteries are in principle the same, only more efficient. Which means different electrolytes and different electrode materials, electrodes placed close together, separated by thin porous material, everything enclosed in usually sealed compartment. All of it to increase the efficiency of ion flow (i.e. the current we can draw), amount of energy we can store and safety. There are 3 main types of betteries: lead/acid (car starters or deep cycle betteries to store solar energy), lithium-ion and & nickel-cadmium (for electronics).
2. Not in a sense you might think. Volt is defined as the electric potential energy per unit of charge, i.e.: 1V is the electric potential you get when you charge an ideal electric system with 1 Coulomb of charge, with 1 Joule of energy. Conversely, when you discharge 1Coulomb and you get from the resulting current 1 Joule of energy, the discharge was occurring at the potential of 1 Volt. Another way to remember what is Volt as a unit is to recall a simple equation from the school
1W = 1A*1V or eqivalent: 1V=1W/1A
So 1 Volt is the electric potential which produces 1 Watt of power when it forces a flow of 1 Ampere of current. Because 1 Ampere is defined as a flow of 1 Coulomb per 1 sec, while 1 Joule is 1 W * 1 sec, both definitions are equivalent.
Said abstract electric system we are talking about does not need to be a chemical battery, it can be can be e.g.
a magnetic force where electricity is generated by induction, This is the most common way of generating voltage in electric power plants.