18 million die each year from "poverty-related causes"
Likely original source: "Poverty and Human Rights" article by Thomas Pogge (published among documents on the site of UN Commissioner of Human Rights).
Accuracy of the claim to that original source: Accurate
Roughly one third of all human deaths, some 18 million annually, are due to poverty-related causes, easily preventable through better nutrition, safe drinking water, mosquito nets, re-hydration packs, vaccines and other medicines
Reliability of the source's data itself: Original source did NOT cite that statistics, although many other stats in that same article are well cited. As such, the data is NOT reliable, being un-cited.
- Caveat: a subset of the data is cited (10M child deaths), but it cites a UNICEF brochure, which isn't exactly a scientific publication and doesn't cite anything itself.
Usage of logical fallacies: Possible but hard to ascertain given the lack of proper citations to proper research. Even if the stat is accurate, this research sounds like makes no effort to attribute the deaths to actual poverty, as opposed to causes that may be associated with poverty. To be clear, that doesn't make the claim untrue, just unproven.
Relationship to the Facebook Post's conclusions
Leaving aside the accuracy of the data or the claim, most of poverty-related-caused deaths clearly occur in 3rd world countries, NOT in capitalist countries, especially if you look at causes listed. As such, blaming capitalism for this is an absolutely false conclusion to arrive at.
Moreover, it can be shown that capitalism was arguably the greatest contributor to reducing poverty.
China (which has never shown any interest in MDGs) is responsible for three-quarters of the achievement. Its economy has been growing so fast that, even though inequality is rising fast, extreme poverty is disappearing. China pulled 680m people out of misery in 1981-2010, and reduced its extreme-poverty rate from 84% in 1980 to 10% now (source)
In case quoting from Cato or Mises Institute sounds biased, let's quote that extreme right winger, Bono:
“Aid is just a stop-gap. Commerce (and) entrepreneurial capitalism takes more people out of poverty than aid. … In dealing with poverty here and around the world, welfare and foreign aid are a Band-Aid. Free enterprise is a cure. … Entrepreneurship is the most sure way of development.”
I left a comment explaining why I'm only addressing claim #1. Mostly because clumping all 4 together is too broad