Shot through the heart, is death instantaneous?

The brain has about 4 minutes of oxygen, so no, a heart shot isn’t instant death*. In fact, depending where the heart is injured, it’s remotely possible to survive. That would only be if sophicated medical care was immediately at hand.

*I have sad personal knowledge of this. My grandfather shot himself in the heart. I was the first to reach him. He was able to say my name before he died.