(a) That's wrong. Sole traders cannot by themselves always do everything that is required to operate a business. But there is nothing to stop a sole trader from employing staff, or contracting for the supply of particular services.
For example, in the circumstances of the case-study, Edward might want to pay an accountant to maintain his financial records, or employ an assistant to help run his office or to help him do plumbing work. Such persons would enter into the necessary contracts with Edward, as employees, agents or independent contractors.
Of course, having employees increases Edward's responsibilities. For example, he would become responsible for making compulsory superannuation contributions for his employees, as well as paying payroll taxes and workers' compensation fees.