Why did West Francia have a hereditary monarchy while East Francia had an elected monarchy? In what way was the Holy Roman Empire not really an empire?

Weren't E/W Francia created at the same time for Charlemagne's sons? Why did they have (at least initially) a different type of succession?

Also, referring to Voltaire's famous quote, why was the Holy Roman Empire not really an empire?

Bonus question: how were the borders of East, West and Middle Francia determined?