“Man’s survival requires that those who think be free of the interference of those who don’t.” I will assume that Rand doesn't mean this literally, for it would be absurd to believe that people who don't think could interfere with people who do. After all, who doesn't think at least on some level? The severely mentally retarded? The severely brain damaged? I suspect what Rand meant to say is, Man's survival requires that those who think well be free of the interference of those who don't think well. In the face of the evidence, this is clearly an exaggeration. Men who think poorly have been interfering with their betters for centuries, and yet somehow the human race has managed to survive. Rand provides no evidence to the contrary because no such evidence exists.
“All the evils, abuses, and iniquities, popularly ascribed to businessmen and to capitalism, were not caused by an unregulated economy or by a free market, but by government intervention into the economy.” Well, at least Rand tried to provide a little evidence for this one in her article praising Vanderbilt and James Hill. Unfortunately, the little evidence she provided is one sided and riddled with confirmation bias. Moreover, a broad sweeping statement such as Rand's requires more than just a little evidence. What about the evils of 14 hour work days? What about the evils of child labor? Yes, I know, Rand argues these things were necessary in the constitution of things, and that the only possible alternative would have been starvation for the workers and/or children involved; but they were an evil nonetheless, nor were they an evil caused by government interference.
“A ‘mixed economy’ is a society in the process of committing suicide.” What does it mean to say "in the process of committing suicide"? The vagueness of the expression makes Rand's statement impossible to either confirm or deny on the basis of evidence. All societies throughout human history have had some form of what Rand would call a "mixed economy." And all nations, except those currently prevailing, have at some point collapsed or metamorphized into something else. Nor does there exist any necessary connection between freedom and longevity. Athens was freer than Sparta; yet Athens' period of freedom was relatively brief; Sparta flourished for seven centuries. History is full of examples of less free societies outlasting, even conquering, more free ones. Nor is there any reason to believe that an "unmixed" economy, assuming such a phenomenon even capable (per impossible) of existing, would not at some point face the tolling bells.