Still, they are problems, and capitalism has no solution - it can't have a solution, because it doesn't offer any solutions, it only denies one proposed solution.
Capitalism has no solution but it does not prevent people from solving these problems. Capitalism, for example, did not create electric lighting, cars, and air conditioning (unless one wants to argue that the economic freedoms offered by capitalism are responsible). These (and many others) are solutions to problems that people took upon themselves to solve. None of them were mandated nevertheless they occurred anyway.
Within a capitalist free market, there is gross injustice. This has already been agreed upon. Some people are born to rich parents who can send them to law school or medical school or train them in some other high-paid profession. Other people are raised by a divorced single mom who can barely afford to feed them healthy food, let alone give them an education after high school. This is a self-perpetuating problem and it leads to a social hierarchy: the rich keep their wealth across generations, and the poor cannot escape their poverty.
I agree that within a capitalist free market there is gross injustice. But this implies that there is not gross injustice in other systems of governance, which is untrue.
However, the examples you cite are not unjust. You are pointing out inequality not injustice. Injustice is evil, inequality is not. Attempts to coercively eradicate inequality will inevitably lead to injustice.
The narrative that the rich keep their wealth across generations and the poor cannot escape their poverty is a popular one but I don't think it is born out statistically. Wealth passed down from generation to generation tends to get frittered away and rarely lasts much beyond the third generation. It is hard to gain great wealth but it is easy to spend. In America (if I remember correctly) over half of the households will at some point be in the top 10% of earners. Of course not every year but this cuts against both assertions.
May I recommend "Wealth, Poverty, and Politics" by Thomas Sowell. Here is an interview touching on some of the topics
https://youtu.be/ICsPQnGJEpY
Within a capitalist free market, there is no way to stop the abuse and exploitation of the earth's resources. We agreed elsewhere that the tragedy of the commons applies to the environment. We are all grabbing as much as we can and destroying rainforests in the process - rainforests that, we have learned, cannot so easily be restored. We are destroying many species of animals which we can never get back. We are throwing so much trash into the ocean that it starts to wash up on the shore. All of this because we are greedy and care more about acquiring wealth than about living sustainably.
This statement seems to ignore the previous statement which was concerned with the poverty of the poor. Are they greedy for wanting to acquire wealth?
"There is no way to stop the abuse and exploitation..." Yes, there is. One simply stops. What you mean is that you cannot coerce someone else to stop if they disagree with your assessment.
I disagree with your characterization that what is driving people is greed. Try not throwing anything away for a year. Zero waste. If you throw something away you are being selfish and destroying the environment. You will find very quickly that it's not so cut and dry. In fact you will begrudgingly throw things away long before the year is up despite that it will end up in a land fill. You will use electricity, and upgrade your computer, and buy groceries rather than become a farmer. It is not because you are selfish, it is because there is a serious limit to what you are capable of doing. Moreover your statement suggests that things are getting worse but I don't think this is accurate. We are furiously trying to solve many environmental problems. Great wealth, time, and resources are valuable for solving these problems. I can hardly imagine starving people in abject poverty taking upon themselves to grapple with such problems.
Within a capitalist free market, there is nothing to stop swindlers from rising to the top.
Sort of. Voluntary decisions and competition will typically make swift work of swindlers. The example of Martin Shkreli is rather amusing. You do recognize that it is patent law that allows him to be free of the pressure of competition? This is why he is able to charge what he likes. He has a governmentally enforced monopoly. If it were up to market forces he would be taken out at the knees. However, we want to preserve and reward large investments in research so we generally agree that patents should be enforced to encourage risky/expensive development. Patents don't last forever. Soon enough it will move into public domain and true competition will cut out the bad actors.
and the fittest are not usually the most deserving.
Maybe not ethically. We are all sinners. But certainly when the market is working the fittest for solving a particular problem are the "most deserving" in that in the collective opinion of the purchasers they are delivering best solution at the cheapest price.