Windows button + R, type "dxdiag.exe" without quotes, and click on the "Display" tab. Under Device, the name of your GPU can be found.
You don't need to install anything to learn about your hardware. I still recommend using dxdiag to see, it's included in Windows and it's much faster.
Best you can get for NZD 500: http://nz.pcpartpicker.com/p/88jBf7 For 600 you can get an i3-6100 instead: http://nz.pcpartpicker.com/p/Z97GmG Should get the i3 if possible, the Pentium might have trouble running some games that need 4 CPU threads.
Forget about it. Lol, high settings... On an Intel quad core, clocked @ 4.5 GHz and GTX 970 I even can't comfortably run all high settings on all maps.
No. If you disable dynamic reflections however you should get 50+ FPS on most maps. Might want to set mesh quality to medium for maps with lots of trees too. I can run most maps @60-80fps, drops to ~50 in ECA town. Don't max out dynamic reflections.