If the tariff of coffee decreases and studies found out that coffee reduce the chance of colon cancer, what will this do to equilibrium price and the demand for coffee?

When tariff decreases, foreign producers are willing to supply more coffee at the same pretax price. Thus the supply of coffee will increase, i.e., the supply curve shifts to the right.

The new found benefit of coffee will make coffee consumption more desirable, hence increasing the quantity demanded for coffee at any given price. Thus the demand curve for coffee shifts to the right as well. The equilibrium quantity consumed will increase unambiguously. Equilibrium price will fall if demand increases more than supply, and rise if demand increases more than supply.