Example 1A: Shoot him dead; find evangelical Christian to raise rapist from the dead; shoot him dead again.
Example 1B: If you are against killing, shoot him in the knees, and then use the butt-stock (or pistol grip) to shatter his teeth. Thus unable to run or bite, once convicted and released into general pop. he’ll learn empathy for rape victims in the state pen. We’ll call it “rehabilitation.” Optional treatment: use third bullet to turn rooster into hen.
Example 2: Show him the loaded weapon, instruct him to never return, and allow him to flee. If he returns, shoot him.
Example 3: This is a comedy of errors waiting to happen… reminds me of Faulty Towers. Let the cops handle this from the get-go. But if you must venture forth, I agree with what Pete said… but if the neighbor hesitates, shoot him. Dead men tell no tales.

1. Definitely.
2. Uh…is this a fetish-style role-play? I think you have to read the situation to figure this one out. Don’t barge in shooting, but if the girl is terrified enough when you question her AND you trust her integrity completely, blow him away. Otherwise, wait for the cops and let them sort it out.
3. Neighbor, by law, doesn’t have the right to shoot if the dude isn’t on his property, so this is a definite no. Although I can’t imagine that someone WOULDN’T stop if they saw any one of us step out of our garage with our various carbines, rifles, or pistols slung about our bodies.

Ex1: Right on
EX2: Judgement call. Reasonable belief of rape, yes (see ex1…) otherwise, wing ‘em…
Ex3: Don’t steal the bike back. This leads to anger, anger leads to hate… and bullets. Instead, consider doing approximately equal financial damage to the thiefs belongings (sort of a modern ‘eye for an eye’, but with $ instead of eyeballs…)

Example1: A guy breaks into a home and rapes a woman, he deserves to be killed.
Example2: Kids making out, girl says no, guy continues kissing etc. Father walks in and shoots him?
Example3: Guy has bike stolen. Knows where thief stores it. He steals it back and is caught by the thief’s neighbor, does the neighbor shoot first?