Runner

[DG]

"If the lead runner is put out for the 3rd out, the following runner doesn't score."

Correct

"But what if the lead runner returns to home safely?"

He would have to touch home before the following runner does. He can't return if the following runner has touched, even if he is in the process of trying to do so.

"How do runs score and is there any out?"

If the lead runner touches on return before the following runner touches two runs score. If he can't make it back before the following runner touches, then he can't continue to return to touch and the defense would have to appeal his miss to get an out, which would negate all scores.