Where to use thermal grease or thermal pad

I used the guide here to help me replace my dc-in sound board. It was great help in the disassembly but what i need to know is. Where is it safe to use thermal compound at or only use a thermal pad at. Reason i ask this is of all the used parts i seen on ebay. They all look like mine, you can see where. There is thermal compound used and to me what looks like a thermal pad. You can see from the pictures here i posted. On the board to the left is the processor which i plan on using arctic silver 5 for. Then in the middle not sure what its called. if someone can tell me it be greatly appreciated. It looks like a thermal pad was used. Can i use a thermal compound here. Then to the right on the Graphics you can see thermal compound was used. Plus you can see how they bridged the thermal compound in a X shape. To make complete contact in all the parts. Here i plan on using arctic mx-4 because its metal-free and non-electrically conductive. Which eliminates the risks of short circuit. Plus i also know there must be complete contact between the heat sink and parts with no gaps. Also since i got it all apart is there a way to check the fans. Other than using some wire and a battery.