Anarchy is democratic, but that doesn't only mean representative democracy. Other democratic forms exist.

Ideally, no single person should be able to make decisions on behalf of other people, ever. There should be a consensus required and reached so that everyone has a say in how they live. Of course, that requires that everyone has a basic minimum level of education and quality of life, that simply wasn't possible in the societies of the past.

I know I would hoard less if I trusted the system for my basic needs. And, if I just get a few more years of good job, I might be ready to stop hoarding (and continue working, just with a lot more mutual aid and independent creator support going out).

But, I just don't think that's true of my father (RIP), or some of the people I met during my time in Northwest Arkansas; none of them even "millionaires" but all having a real drive to squeeze another penny out of every nickel. And, as you say, we have billionaires: any of them that aren't just handing out money every waking hour are not behaving ethically.

I just don't know that one the scale of 8b people, or even 300m people, that there aren't enough natural "hoarders" to ruin everything. But, I'm also sampling from as experience where everyone I meet is steeped in the "water" of Capitalism from the cradle, so maybe there'd be fewer natural "hoarders" in if Captialism hadn't soaked into us before puberty.

I wish that were true, but that simply does not align with my experience with people.

Are there people who would be satisfied with their basic needs being met? Yes, but I believe they are a small minority. The small percentage of people who are billionaires is not representative of all of the people who want to be, just the people who wanted to be AND SUCCEEDED. You do not know the names of the vast majority of people who have succumbed to greed and tried to become that wealthy, only to fail.

A huge factor is social status. Most people I see around me are highly concerned with how they are perceived by others. They want the job title, the bigger house, the bigger car, the expensive clothes. They want to be seen at the exclusive clubs and restaurants. They want the latest videogame console, to watch the latest movie and TV show, and be able to talk to other people about all of the #content they have consumed. That's why all these billionaires have mega-yachts - it's not because there is some correlation between sailing and business accumen, but because all of these wealthy people are using their megayachts to schmooze and show off to each other. It's why billionaires are starting to get into space travel. Most people want external validation and status over others.

Until we find a way to solve that as a species, I think we need either systems in place to prevent hoarding or we end up where we are today with the terrible consequences of wealth inequality.

Are we expecting everyone who feels that their rights have been violated to be responsible for their own justice?

No, you are called to defend not only yourself, but others as well. Everyone is responsible both for their own and everyone else's justice. If you are more capable and willing to produce justice, you may produce more than you need. In many ways it is like all the other requirements of a good life: excess freely given, unmet need freely taken.

If someone wants to fit into some "heroic police officer" or even "hero vigilante" role, they will likely be celebrated and supported as long as their actions are heroic, but if they take any bad actions they will be reprimanded and resisted; they chosen role will not be a justification or mitigation.

How do you does anyone actually stop them?

Threats of violence are allowed to be neutralized by whatever means, including preemptive, defensive violence. All actions should be for the collective good, even as they are done by individuals. Collaboration, communication, and coordination are encouraged in whatever form the individuals find is best.

I think a lot of what is done depends too much on specifics to make general statements. But, anything from a strong talking to next time the offender interacts with the community to assassination to revolution-scale secretive, cellular, violent action might be justified.

Who judges this in an anarchist society?

Each person is their own conscience. Anyone may arbitrate, and others might comply or ignore it as their conscience dictates. Arbitration might call for violence, and if executed, that violence will surely be judged in turn.

But what about the more abstract violence? In modern times, who do we stop people from mining and burning fossil fuels?

Despoiling the commons is considered anti-social behavior and is subject to resistance. Generally this will start with a discussion, but if consensus can't be reached, property damage (e.g. destroying tools and/or machinery) will stop the worst effects with no "crimes against persons". But, persons or organizations that purposely and repeatedly engage in anti-social behavior will be treated as if they were the government and resisted potentially violently.

High marginal tax rates funding social programs has, historically, worked. Part of what is necessary for it to work though is the collective and organized threat of violence

I don't disagree. I'm all for bringing back to 92% marginal tax bracket, getting rid of corporate welfare (particularly for petrochemical companies), and really building a safety net that ensures no one has to go without food, water, clothing, and shelter, whether they can work or not. I can defend anarchy while still working within the existing systems. Sometimes the best way to the goal actually is building up something you later will choose to tear down.

I'm not even a committed anarchist, but I know that all of your questions, and every "gotcha" question for anarchists I've ever seen, has already been considered and answered in anarchist theory, sometime many, many times -- often even refined through the practice of anarchist societies.