I'll attempt an answer :
Does anyone know the system we live in?
Descartes said that the only thing one can know for certain is that one is thinking.
That is, one can be certain that one's mind is perceiving the world, but not that the world exists in any physical sense.
To some this sounds risible initially. For example when confronted with this concept Samuel Johnson kicked a stone and said 'I refute it thus'.
What he meant to demonstrate was that kicking the stone (interacting with the real world) resulted in pain, and that pain (and that his foot didn't pass through the stone) was proof that his foot had interacted with something physical.
But of course, pain, and 'solid objects' could just be imagined, like everything else.
To put this immaterialism in a contemporary context (as you already have) we can imagine that the world is a simulation fed directly into our brains, as in the film Matrix. In the case of the Matrix, what is the matrix? It's a computer construct.
And in fact the idea that the universe is a simulation is called 'the simulation hypothesis', or 'simulation theory'.
The probabilistic nature of our reality as described by quantum theory is worryingly congruous with the idea that reality is numerically simulated.
What happens during brain surgery, general anaesthetic or use of hallucinogens? Our perception of reality is altered.
Is this evidence that our minds are in some way connected to reality (that our physical brain produces consciousness?). Or are we temporarily seeing a new reality, or just imagining the acid trip?
It may be that 'idealism' is like pink unicorns, just a thing humans are capable of imagining that is irrelevant in reality, just as the joker cards are part the deck, but irrelevant for the purposes of most card games.
How can we know what things the mind can imagine are relevant?
Well we would have to start by simply ignoring pink unicorns, until we discover one.
Science is a system of learning which relies on experiment.
That is, a theory cannot be accepted as 'true' in science until it has been shown to be repeatably true 'empirically' by several different people.
Philosophers argue about what constitutes knowledge but science has a definition which appears to work (to deny that science is effective is just absurd).
To a scientist (for the purposes of science), it really doesn't matter whether the universe is a simulation, or in some way immaterial. All that matters is that our perceived reality seems largely predictable.
And so science has restricted its activities to examining the predictability of reality.
Through this epistemologically restricted process science has learned to control and understand fundamental aspects of reality (electricity, magnetism, light, sound, chemistry, biology....)
This catalogue of knowledge explains what our perceived reality is.
It could be that the description of reality that science gives us, not only accurately describes what we perceive, but describes reality itself.
It exists. Why does it cost others their lives like Socrates?
I'll take your point to be, Socrates was killed by other people, because they didn't like what he was saying.
How can one be killed by people one is simply imagining?
How can a person disappear (die) from our world, if our world is not physical?
Again there are two real answers :
What is death?
If the world is a simulation or in some other way immaterial, then what is death?
Does one's mind simply move on, into a different reality?
Is it arrogant to imagine that other people may not be real, because they are part of MY mind? If I die, will those people cease to exist?
Reality isn't nice
Why must all living things die anyway? Science says this is somehow related to 'entropy'.
Why do humans murder, or cause the deaths of other humans? Well because humans aren't very nice?
How can we make a better world, in which humans are nicer. Well that relates to your last question.
Lastly, do philosophers know what to do?
Political ideology is essentially philosophy.
Just about everyone can imagine a better world, but what they consider to be the problems of this world differ almost infinitely.
Some believe that life is simply a struggle, and that one should just get used to the idea early in life. Concentrate on ones own circumstances, and ignore trying to change the world.
Others say point out that things are improving BECAUSE humans have tried to change the world, and that we should continue to do so.
Despite having hot running water, and mobile telphones.. humans are still hitting each other on the heads with sticks.
We are still fighting wars. We are still subjugating others.
Our technology makes life increasingly comfortable but nothing is really changing, and nor will it change because humans are humans and can't be anything else.
Asking for change would be like asking a dog to become a bird.
Not until mankind transcends the human condition will anything change, and that would requre a new kind of human, that is different from current humans.
The most pessimistic say that nothing will change until a new type of human literally exists (is engineered, or born by chance). A small minority of 'superior' humans (philosopher kings) will assume control and make everything better.
Others believe that the human ability to 'behave' and 'be civilised' is all that's required to transcend the human condition. That is, people simply need to become, behave like better people.