You are quoting from a section where the Pharisees are attempting to trap Jesus. To say "put her to death" would subject him to Roman law (only Romans could execute people in the territories they controlled). To say, "let her live" contradicts God's law and the Pharisees could use that against him with the people. He didn't contradict God's law and stayed within the confines of Roman law by using the answer he gave. Again, mercy is allowed.
What does having mercy have to do with "whether or not you can morally kill a person?"
I ask because something odd occurred to me. Jesus only really grew enraged and lashed out physically once. That was against the merchants defiling the temple by selling their wares. And you talk about how you are allowed to defend yourself.
Now this is off topic, but why then does Jesus not "follow his god given right" to defend himself. By killing Judas or the men who were certainly coming to hurt him?
If turning the other cheek is something we strive to do, yet we can apparently morally kill someone why wouldn't the person whose example we follow do so?
Also this is a strange line of thought. You say you would kill someone in self defense. Doesn't that mean you premeditated it? You are saying "if this happens, I will do this." That is a planning, well more assuming you actually have the balls to actually take action... Is instinctual programming not in a sense premeditation. When this happens I will do this?