It is different industries that are put into categories based on the market for goods and services. Business structure is how the business is organized.
Is it possible for a sole proprietorship to be in a monopolistic industry?
Yes actually there only really in a monopolistic competitive industry.
Is it possible for a sole proprietorship be in a perfectly competitive market?
Yes, it's actually one of the main business types in that market and they do very well.
Is there ways that a corporation can become a monopoly?
The government actually grants businesses the ability to sell certain products.
Are there ways a partnership could become and oligopoly?
A partnership is just a business with two or more owners so that just means they split that profit with one another!