Our family already has an xav2001 powerline adapter plugged into the router and another one in my brothers room. Is it possible to add another adapter for my computer, and if so, does it have to be the same model as the ones already installed?
You can add another powerline adapter. They will share bandwidth between the multiple adapters. That is an EARLY model of powerline adapter. If you are going to add to it, I would recommend updating the original pair at the same time. Powerline has gotten much better in the last year or so.
My powerline adapters allow up to 4 adapters. Have a look in the instructions, just make sure you get the same model. Although they should be interchangeable I had issues mixing two trendnet models