The CPU is not supposed to come out with the heatsink, but it happens with some types of thermal paste. I usually give the heatsink a slight twist to break it loose from the CPU before I lift it up. You should be able to gently pop the CPU off the heatsink (if you need to pry, use something that won't scratch either the heatsink or the CPU heatspreader), clean everything up, reinstall the CPU (after checking for bent pins), and reinstalling the heatsink with fresh thermal paste.
As for your graphics card, are there any power sockets on it? If so, power cords need to be plugged into it since the slot will not provide enough power.