Do CPU, GPU, and motherboard coolers have to be "compatible"? If so then can somebody tell me how to know if they are compatible and a few suggestions. Thank you
Only the CPU has a heatsink (cooler) that needs to be compatible to that CPU and that particular motherboard on which it is installed. Usually the heatsink will list the motherboard sockets that it is compatible with,
The GPU has a self contained heatsink that the user need not worry about.
Many coolers fit a broad range of CPU's, you need to match the cooler to your socket, however SOME motherboards are tight so some coolers could interfere with heatsinks or even memory slots, and you need to be careful of this. There is no formula for this. Its hard to say for sure but asking the question here is helpful as some guys may have tried a cooler on a board and found it to not fit right.
The CPU cooler you chose has no relation to the GPU, you don't need to worry about that.
"Do CPU, GPU, and motherboard coolers have to be "compatible"? "
I guess the key word in the question is coolers, but still I don't get the question entirely. Can you elaborate a bit?
Only the CPU has a heatsink (cooler) that needs to be compatible to that CPU and that particular motherboard on which it is installed. Usually the heatsink will list the motherboard sockets that it is compatible with,
The GPU has a self contained heatsink that the user need not worry about.