The PSU is fine for that GPU and CPU. If you're going to upgrade in the future, you could get a 700 / 750 PSU to be on the safe side, but a 600W PSU is OK for what you're proposing.
Interesting that the mobo doesn't recognise the CPU but still works with it. For safety, check the voltage and temperature it's running at to make sure the chip isn't going to end up damaged.
i checked it and the temperature reads Tj Max 70 C, Cpu#0 34 C and core voltage 1,424. Is it alright ?