You can check the following website http://cricos.deewr.gov.au/ , it contains all regiserted institutions and courses.
All international students are protected under ESOS Act.
This really depends on student visa condition restrictions and school sector you are looking for. It is recommend to consult with experience migration agent in order to determine your are eligible to change education sector or education provider.
It is ok for you to add your de facto boy friend to your student visa application, it is important to know how to demonstrate your relationship is genuine and continuously. Time of your study and financial are also important in your application. We are happy to instruct you to prepare your application and ensure your application to be granted.