(a) That's wrong. It is true to say that the facts in the case study mention three different contracts. Miles has entered into a contract of purchase and sale to buy the new packaging machine, but that contract is not with Peter. It is also very likely that a contract of employment exists between Peter and Peter's assistant, but again, that has nothing to do with Miles.
As between Miles and Peter, the contract is one in terms of which Peter promises to bring about a specified result (the installation of electrical equipment) in exchange for a payment of money. This contract is best classified as a contract to provide services, Peter acting as an independent contractor rather than as an employee. The facts do not in any way suggest a contract of lease.
What is the difference between a contract to provide services as in independent contractor and a contract of employment? The question to ask is whether the person who agrees to do work is to become a member of the other party's organisation or enterprise.
In the current case, Peter does not become part of Miles' business. It is clear that Peter will carry out the agreed task in the way, and at times, that he himself sees fit, rather than keeping regular office hours determined by Miles. Further, Peter provides his own materials and equipment and is to be paid a lump sum for a specified task, rather than being paid a salary.