I am having problems with my Powerline adapter which TPG does not assume responsibily for.
So I am going to buy a new router with better range so it can reach my PC which is far way from the current router.
Am I allowed to buy a router and use it with NBN 50?
You can use your own router but if you use TPG Home Phone then you need to retain the TPG supplied router. If this is not important to you then no problems.
Rather than trying to reach a point in the house using just a better router I would suggest trying
a product called WIFI Mesh. There are multiple vendors selling these items from 1 Pod to 3 Pod systems. Rather than broadcasting Wi-Fi signals from a single point, mesh router systems have multiple access points. One point connects to the modem, while one or more other access points, often called satellites, capture the router's signal and rebroadcast it. All pods are running the same SSID so unlike Range Extenders you do not need to manually swap between SSID's when you are in that location. The downside is that they are not cheap, but if comparing them to a High end router they are very comparible in cost. The benifit over a Mesh Wifi sytem compared to even that high end router is that you will have a much greater wifi coverage area.