A drowning victim will instinctively push the rescuer under the water, so the rescuer must have a secure flotation device. It was (probably still is) taught to pull the rescue-e to land by having the victim facing away with your arm around their neck and under the armpit facing away. This is to keep them from drowning you.
This is also biblical - take the splitter out of your own eye before you take the splinter out of another's eye (paraphrasing).
Not necessarily. It's called empathy. And your lifeguard story makes no sense.