Well some of your questions are stated poorly so I can't really understand them. By look at the title, "quadcore compatibility", sounds like you are asking about Dolphin using 4 cores. If so, Dolphin will only support 2 cores, no more is needed.
:: System Specs ::
Operating System: Windows 7 Professional x64
Video Card: ATI Radeon HD 5770
CPU: AMD Phenom I X4 9550
RAM: 6GB DDR2
EXP Index: 999999.999999
Operating System: Windows 7 Professional x64
Video Card: ATI Radeon HD 5770
CPU: AMD Phenom I X4 9550
RAM: 6GB DDR2
EXP Index: 999999.999999
