Clarence Carson was a Ph.D. historian who taught history at several colleges including Hillsdale and Grove City. He advocated liberty, though he was not a libertarian.
On your first point, it’s not uncommon for economists to assert that government as defender of person and property is a precursor to the market economy. Ludwig von Mises makes the same claim in his book, Human Action.
On your second point, there are good points on both sides of the debate over whether or not to call the market economy “capitalism.” Historians tend to define “capitalism” as the historical system of government-business partnership that emerged in the West in the mid-nineteenth century. Karl Marx himself coined the term on the grounds you mention (it’s the system that favors capital over labor). On the other side, “capitalism” does describe an essential feature of the market economy, namely, that entrepreneurs can calculate “capital value” and thereby, efficiently allocate resources and invest in capital capacity.
Carson was not an Austrian economist, but his views on these two points don’t contradict Austrian economics.
More thorough introductory treatments of Austrian economics are David Gordon’s, Introduction to Economics Reasoning:
And Bob Murphy’s, Lessons for the Young Economist: