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it really depends on what you mean by no rules. It is more the ideology of putting no artificial construct above humanity, like law, capital, etc. One of the worst parts of capitalism is alienation from the product of your labor, so one of the more important aspects of communism is having more impact on your personal environment. That does not mean people will not react, however, so you can't go around hurting other people without repercussions of some kind. In fact people will be more free to react.

"rules" aren't really a concept outside of a monopoly of force by a state-like entity, so there isn't really a good explanation of that specifically. It's like asking about the properties of a square when using a circle smh

Could it be said that there are no rules then?

I don't think the concept of rules applies in this situation. The idea carries a lot of assumptions with it that simply don't make sense in this type of society. It's like asking what the radius of a square is imo

So how do people know what is allowed and what is not allowed?

you have the ability to do whatever you want with the tools you have. The question is what the impact will be and if others will try to stop you. There isn't some god telling you what is and is not allowed, it completely depends on the situation.

Are you asking how people would react to your actions? If they would structure it in a specific way?

If someone kills another person, how do you resolve the conflict that could arise from there? If someone sexually abuses another person, say a child, how does society proceed in that case?

there is no set way to proceed.
https://theanarchistlibrary.org/library/peter-gelderloos-anarchy-works
That book goes over cases in history where systems like this were in place.

What I would do is tie the person up, call a town meeting, and decide what to do from there. Maybe I won't have enough time, and my only solution will be to shoot them. It all comes down to the individual decisions of those involved. Some might not call a local council, some may create a specific force dedicated to this. Who knows