How can I print a list of student addresses including their postcode, as well as find a student using their address only?

You can obtain students addresses, including postcode, if you go to Reporting > Reports >Students (tab) > Addresses. When you have created this report, you are able to type in the address in the white box under the address column and it will take you to the student. 

You also have the option to show Small Address or Expanded Address. 

When you select Small Address, the address will all appear in one cell.

When you select Expanded Address, each field of the address has its own cell.