Claims 1 and 2 are false on their face, because (as you point out yourself) the execution is equivalent.
You don't typically need to control order of application of the function to the items, which is why it's fast. You do of course need to control order of function application, but with function syntax it's all the more clear.
Optimization meanwhile is the same, except for the most degenerate of examples such as "we hand-crafted the machine code of this operator for this one case".
But a typical implementation of combining two arrays in all permutations would be something like
permute(NIL, a, b)
so the compiler can see that there's no action required but to combine them, and it's a trivial matter to parallelize the combination across N cores or computers. Indeed there were functional compilers capable of fully optimizing this problem in the early 90s.
As for item 3 I will have to say that I doubt you are right, but I cannot claim either way since there is of course no evidence presented, and probably no research.
I do find infix to be pleasant for colloquial, familiar expressions. I find it to be personally extremely counterproductive for comprehension with unusual constructions.