I specify 1/2" hose for the connection between the header tank and the coolant pump to accommodate "surge" in the cooling system, which occurs when the speed of the engine rapidly accelerates or decelerates. I don't know if anything would happen if you decreased the size of the hose, other than the fact the level in the tank "may" be a little less responsive to surge. I was just being safe.
3/16" ID hose (or 3/16" OD metal tubing) should be fine for the air bleeds in the cylinder heads.
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