If I am making fried liver tempura style should I pre-cook the liver? I think when you make an item like, say, shrimp tempura, the shrimp is cooked beforehand because the tempura frying is not sufficient to fully cook the shrimp. Is the same true of liver?
It's not exactly the same for liver, but there is some reason to roast it before frying:
Some people believe in roasting (grilling) before the cooking/frying in order to make the blood drip out of the liver. Can do on fire or in an oven; doesn't matter.
Personally I prefer to go directly to the pan and just fry so it gets less dry. It is definitely sufficient cooking for the liver.
Unlike a heart which would only include residual blood, other organs, especially digestive and some of the defecating body organs, often need extra steps to prepare (eg: kidneys--try cooking them without at least a presoak). Therefore, I would either cook the liver first, or at least marinate it in a vinegar based marinade.