Gandalf died after killing the balrog because he broke his staff but more because without it he collapsed from exhaustion.
no actually the staff although imbued with power is more likely a lightning rod of sorts Gandalf has the power within himself but its unfocused like electricity or radio waves going every which way but the staff like an attenna or a wire controls where the magic goes gandalf when he came back had more power yes and received a staff that could handle the power on the bridge he sent so much power through the staff it shattered like a fuse after a powersurge