Golden Sun and Golden Sun: The Lost Age are both chock-full of battles, and with battle, usually comes death. But is it death? There is evidence for both answers.
In battle, a member of your party can have his/her health points reduced to zero. Zero Health would typically be thought as death. But your party is still there, just knocked out, or more appropriately, downed. Monsters appear to Die, for they melt away into dust during battle. However, the same thing happens to people in scripted boss battles, or any battle for that sort, that contains characters. For example, in Colosso Finals, or the Bandits of Vault, or the Guards of Lunpa Fortress, or Saturos and Menardi, they lie on the ground, not dead. More evidence to the fact that one does not kill in battle is the fact that you "fell" monsters, not "kill". The game text displays: "you felled*enemy*!", not, "You killed *enemy*!".
Also, some characters do not ever turn to dust after their health points are reduced to Zero, namely wild Djinn. After battle, they jump right up and join your party, perfectly fine, though unable to fight. This is further illustrated as when Isaac or Felix are felled in battle,and when they walk around out-of-battle, they hunch over and stoop, as if exhausted. They can still use psynergy, walk around, even hop, but cannot battle.
So it would seem that there is no death or killing in Golden Sun. However, there are at least three scripted deaths, Saturos and Menardi at the top of Venus Lighthouse, but they are weak and fall to their deaths, and are not felled in battle. The one death that does indeed happen right in front of the player's eyes, however, happens on the road to Venus Lighthouse, when your party comes across a soldier lying on the ground. Talking to him lets you hear his last words, and he dies, but not talking to him leaves him there forever. So this death is optional, depending on the player's choice. Also, Babi dies in The Lost Age, but this happens neither in battle nor where the player can see.
Opinions differ on this, but the only time when a player directly causes a NPC to die is the Venus Lighthouse Guard. If the player talks to him, he dies, so this could be considered as the player killing him, because if the player leaves him alone, he lives. This then brings up the debate as to whether it is more honorable to go to him and hear his last words or simply abandon him and let him waste away there.