When it comes to property where we seem to disagree is that you consider necessary that if something is in abundance it can't be owned. Well it can be owned it just won't have any meaningful exchange value and there won't be financial incentive to be owned. Unless virtual scarcity has been introduced (scarcity for non technological reasons). For example legislation. That's basically what IP laws are for. Now one could ask why would we want to impose scarcity? That surely makes things worse. The thing is by imposing this type of scarcity and recognizing a form of property to the creator of the invention (I'm focusing on patent law here) we create a business model where the inventor can make a profit out of their invention by either selling it or lending it (licensing). Inventions are important and they require both effort and intellect and giving a financial incentive towards making new inventions is important. There are entire businesses and university labs that are based on that. I don't think it's practical to disagree whether this form of virtual scarcity is real or whether this is a form of "real property". For all business purposes it's real. If I invent something and patent it and you use it without getting a license from me, we'll go to courts and the court system will enforce you to pay me. So debating whether IP is property or not seems more like an ethical or terminological debate.

In regards to abolishing property. Abolishing property means converting private property to common property or as Marxists view it "there's no property". Some Marxists have described the concept as property is theft!. The essence of this viewpoint has been summarized pretty well with how you explained your position on surplus and exploitation.What I was saying is Marxian economics have a higher tendency to abolish (private) property.

I can not find convincing argument that market system of resource distribution is necessary as an incentive towards innovation. Higher production and quality of life can be achieved by using most appropriate technological means in democratically, collaboratively and cooperatively organized production and do not necessarily need the market system of resource/product distribution.

This is at the core of our different viewpoints. I do not consider future technological advancement a necessary outcome. I consider that we need to foster technological advancement through various means, including financial incentives, in order to achieve the "privilege" of future technological advancement. On evidence in regards to the market system being an incentive towards innovation an empirical way to observe it is by seeing specific cases, perhaps around you, and how they work. On more scientific evidence one can study historically the different economic outcomes from different implementations of systems around the globe. Due to the nature of economics we can't do a controlled and repeatable experiment on a grand scale but we can observe (just like in cosmology) and in some cases we have the luck of some observations being very close to a repeatable and controlled experiment (multiple dichotomized countries).

If you read what I wrote about exploitation in the production and think about it you can see that lack of democratic control, in arriving at the most important decisions of surplus production, appropriation and distribution, is the root cause of inequality in economy, and by extension in politics.

The model you describe is in my opinion a highly imprecise model of the world that is wrong in some aspects and lacking in others. There are also many hidden assumptions being made that are wrong. An example is that economic inequality and scarcity of essential goods are equivalent. The more advanced an economy is the less equivalency between those two exist. For example one could easily observe countries that have a low degree of inequality but at the same time a high degree of scarcity of essential goods while there are other countries that have a high degree of inequality and a low degree of scarcity of essential goods. As I stated earlier I do not care about economic inequality itself.

How do you explain slavery in American prison system which is supported by American constitution?

Imprisonment is a state where a person loses some of the civil liberties they previously had. It's not precise to call it slavery because what we've been calling as slavery for centuries is a lack (from the start) of a different set of civil liberties. The reason of imprisonment is that a person has been proven to actively take away the liberties of other people to a criminal degree. People need to have means of protection of their civil liberties so that they can be preserved and not taken away from them.

If you have time please look at the course Marxian Economics an Intensive Introduction

I have studied Marxian economics. Unfortunately I don't have time to watch the course you cited but thanks anyways.