What is the difference between, say, eh...

Hypocrite has been misused too often, especially in modern society where people toss it around as an insult. Hypocrite is purely a person who is currently espousing beliefs that he/she does not follow.

In your first example, the "hypocrisy" seems to be that bad people can't do good things. Now, if Jackson went and robbed a store right after stopping that robbery (especially if he preached on about how bad robbery was) then he'd be a Hypocrite. Having killed people earlier has absolutely nothing to do with robbery though, he could be a drug dealer who doesn't believe in letting people rob stores... the only thing that matters are his beliefs on robbing stores, nothing else.

If I understand the situation correctly, the villagers raped a girl and pegged the blame on Henry Niles... where is the hypocrisy?

Don't know about the clockwork orange.

You seem to be referencing a femme fatal, but again failed to explain what the hypocrisy actually is. Is she saying that doing bad things to men is bad and doing them anyways, or just complaining about how hard life is and stepping on the men to get what she desires? I'd argue that the double standard isn't an example of hypocrisy, it just shows that what is being argued for isn't equality but instead a shift in social power.*

*Though, I'd concede repeatedly claiming that you want equality when what you really want is a shift in social power is hypocritical, and that many individual arguments can be shown to be hypocritical (such as with circumcision arguments, if genital mutilation is bad then it should be bad regardless of what sex you are)... but in general what is actually preached is that only female genital mutilation is bad and that male genital mutilation is perfectly fine. Or that only women need some law change and men don't. The hypocrisy happens when you use the same argument made by the feminists in support of a male issue, since you'll see the same attacks masculinists make against feminist arguments being made.

Now that you mention it, the English language is missing a word!

So a hypocrite is someone who goes around claiming to do and believe in good things, but who actually does bad things, or things they've just said are bad. But there's no word for someone who does bad things or claims to be bad, and then turns around and does something good!

Well, there's "anti-hero", but that's only used to describe fictional characters, and leading characters as that. There's no word for fictional supporting characters who turn around and do good stuff to everyone's surprise, or for a real-life bad person who does something good once in a while.

These people are evil, but aren't claiming to be anything else. So when they do a good deed, they're just trolling. They're still sociopaths, and wear it with pride.

if we allow that among humans, there is a large variation in behavior, that people who do bad things , large & small, may also do good or even heroic things, large and small - then the complexity is addressed.

hypocrisy may be understood as, at least, among :

professing one thing while doing another :
https://www.nbcnews.com/feature/nbc-out/secret-gay-life-married-family-values-lawmaker-was-not-so-n823056

projecting a conventionally 'upright' image while being, in practice, a villain :
https://www.nytimes.com/2008/12/13/nyregion/13madoff.html

In A Clockwork Orange the "reformed" Alex was the product of psychological reconditioning. If I recall correctly, he voluntarily submitted to the treatment because he saw this as a way out of prison. I never got the impression that he did it out of remorse.

When he became repulsed by violence, it was the treatment kicking in, not because he now saw these actions as immoral. I guess he could be considered a hypocrite.