There's two parts to this:

1. How do you prevent the people with arms in your community from banding together and taking over? Well, I'd imagine you'd spread defensive readiness across different sectors of your community, embedded within the populace. You would complement seasoned volunteers and appointed or elected leaders, probably with some measure of training for all adults. Ideally you would rotate your soldiers across communities too.

2. How does a society prevent a different society from gathering enough strength to conquer them? I don't know, that's an open question. Once any society has figured this out we can talk.

I would call the people who have volunteered to defend the community. Anarchist societies would still have institutions and organizations - but they should be organized as least-hierarchically as possible, built by the community democratically.

Anarchism is a set of ideals and organizational principles, not some utopian end goal.

The local defense council would be a group of people elected or appointed by the community who are responsible for training, arming and organizing members in the community. How specific are you asking? Like what level of detail would convince you?

What stops you from doing that in hierarchical societies? I mean, powerful people in our society use their wealth and power to inflict terrible pain and misery on the poor. So, what's stopping them?

I would defend my stuff myself or get my neighbors to help me or call the local defense council, sure. I mean, what stops you from doing that now? I see shit get vandalized every day and cops don't seem to do anything about it.

What parts of the "social-psychological nature of the human mind" prevent which aspects of anarchist organizing?

Anarchism as a political philosophy strives for non-hierarchical cooperation. It's hard to say what an "end-stage" anarchist society would look like - anarchism focuses more on how people should go about organizing than the results of the organization.

I tend to imagine society organized across geographies by trade and industrial unions and in localities by consensus-driven democracy with local councils handling the day to day administrative tasks. The economy would primarily function almost as a gift economy, possibly with some markets for luxury goods.