RE: What will the world look like without rich people?
There's nothing harmful about what you're calling communism, but I don't think it's helpful either. If I can persuade you to work with me in building on the land to attain mutual goals or you can persuade me to work together in planting that's great, but basing a social system on the idea that everyone will just have the same goals and agree on how to achieve them together isn't useful. It denies the problem rather than offering a solution. I expect that what you actually mean by communism is much more detailed than that.
I propose that the right of the first user to own the resource should be respected until the resource is either abandoned or voluntarily transferred to a new owner. If I've already built something and the land and structure are not abandoned, you should not destroy the structure to plant. If you've already planted and have not abandoned the land, I should not destroy your crops and build.
Should two or more arrive simultaneously at a resource all desire to use exclusively, they should attempt to resolve the conflict among themselves through peaceful persuasion. If this fails, they may be able to agree on a mutually respected third party to resolve their conflict for them. When people are unable or unwilling to resolve conflict through peaceful consensus, violence is inevitable as the only means of resolution not dependent on any level of agreement.
The most controversial issue in all of this I think is the criteria for determining if property is abandoned. This is where I most conflict with some of those who call themselves capitalists. I don't think there's a perfectly clean logically derivable answer to this question, but my answer to this is based on the idea that the owner of property should not externalize the cost of determining ownership onto potential new claimants. In the absence of any indication that a resource is already part of another person's plans, there is no obligation to prove that the resource is unclaimed before claiming it.
I dont expect folks to agree on everything, many things will have to be worked out by those involved.
For me to make blanket statements about what they will do is presumptuous, and violates the priniple that they have to work through their own problems.
It appears that we are of the same mind on this.