Is it possible to imagine humanity without a modern understanding of money? Of course we can't just take money from current world order and give nothing back.

In theory, can an advanced civilization exist without money at all?
May be this is an utopic idea because of... what? Intraspecific aggression? Our education system? Our history or heritage?
What stops us to do so or to go in that direction?
Is it good or bad in long term?

You need stuff – you take it. You don't need "golden toilet" because of marketing don't try to sell it to you, because "business minds" will be busy to solve problems (or to coordinate other minds to do so), not to make more businesses and make more markets.

The main purpose of this question is to understand what fundamental economics and/or cultural (historical) problems tasks do we need to solve to use more science and less marketing in our lifes.

I have an opinion that we need so much things to buy, sell and choose because of culture, lack of education and a lots of marketing around us.

Marketing needed for business, but not for humanity. We, as a species, spend so much resources of our brains and planet to solve small things (not all of us, of course). And this stops us from doing really BIG things.
The rather famous political economist Marx claims that the wage labour relationship contains within itself the transcendence of that relationship. This is in part as the only socially productive property a worker has consists in the giving away of themselves for a mess of postage.  This suggests a non-engagement with owning socially productive property and instead an emphasis on usufruct. Similarly the commodities of the wage are used (consumed) rather than hoarded.

In Marx’s suggestion that the proletariat can abolish itself, the wage, profit, Capital—in general “the value form”—the abolition of money as we understand it in Marx or contemporary use would necessarily be abolished. Movements of socially useful stuff and services would somehow work on the basis of capacity and need. There might be a mediator, but it wouldn’t have the current functions of money.

Apart from a few very short term instances during revolutionary crises, and generally without ordinary productive activity, there’s no empirical evidence for these relationships; and, there isn’t sufficient material to move beyond large weak concepts like “love,” or “solidarity.”