The technical means given in Part I (reviewed above) are used here to solve some metamathematical problems of AST and higher-order arithmetics. It concerns mostly the consistency of negations (and hence independence) of various schemes of choice for classes, the consistency of the negation of the axiom of constructibility, and the addition of a new (larger) well-ordering. (The consistency of positive versions are demonstrated by A. Sochor [ibid. 26, 477-498 (1985; Zbl 0583.03040)].)
There are no original systems of conditions and no new “normal filters” in the paper, but the method of levelling in the last section is quite original for me.
If understanding some assertions literally (in the last section), they are incorrect. But they can be corrected by the context. Also, some misprints can be corrected in this way. The chosen style of exposition helps. Despite of this, these mistakes make reading of this nontrivial paper more difficult.