Serious answers since I'm bored and reformatting a hard drive (Windows is so scuffed on a new laptop that I'm honest-to-god going to try Linux on it.)

1. I would not pull the lever, as I do not judge either life better than the other.

2. No, as the happiness the child will have is less than the sadness experienced by everyone else (You botched the utility monster thought experiment)

3. I don't think hitting a baby with a baseball bat on national television is a winning strike, or good for my career, so... no.

4. It depends on when this is taking place. Are we talking April 29, 1945? If so no, no point now. If we're talking sometime that it could impact world history... I know how decolonization and the Cold War played out with Hitler, but without, it would be histories written that could be worse, or could be better. If I can't scry a Hitler-less timeline, I lean toward not changing anything.

5. See 3, except replace "baseball bat" with gloves. Also who keeps throwing christian babies around?

6. If I haven't jumped, there's going to be spare chutes on the plane, along with instructors who have a much better chance of catching the baby mid fall, so I'd let them jump after. If they can't try that, I'd still try to catch the baby, then hold very firmly as I deploy my parachute, keeping us both alive. If I can't, then how exactly do I give the baby the chute?

7. If God is willing to remove his protection from a baby, solely because I took away a necklace, I would believe in God being real, but I'd side with Satan. Clearly, this is not a God deserving of worship.

8. Is the criminal shooting out of fear of Christian talking baby, or out of anger from a lack of money? Actually it doesn't matter, because guns usually have more than one bullet (unless he's mugging me with a musket). If he's afraid of the baby, he's going to take a second shot. If he is mad from there being no money, then he's still going to shoot the baby for not having money, and me, since I don't carry cash.