2 What is the case, the fact, is the existence of states of affairs.
Black (p. 39) says that it might be better to speak of the holding of a fact than the existence of a fact. He prefers ‘atomic fact’ for Sachverhalt. A Sachverhalt is “the objective counterpart of an unanalysable contingent truth (see, for instance, 4.2211)” (pp. 39-40). However, Black notes, Wittgenstein uses Sachverhalt in seemingly inconsistent ways. E.g. most of the time he uses it to mean an actual combination of objects, but he also sometimes uses it to mean a combination that does not exist (e.g. at 2.06 and 4.3). Stenius (p. 31) says that “a Sachverhalt is something that could possibly be the case,” but 2.0124 talks of possible Sachverhalte, which would be odd in that case. (This objection is Black’s, as is the page reference in Stenius.) Black argues (pp. 41-45) quite convincingly that Sachverhalte should be understood as facts rather than possibilities, at least most of the time.
My original comment: This seems odd. Shouldn't it be "the existence of a [or the] state of affairs"? Or is the fact that states of affairs exist? Is the world the existence of states of affairs? Or is it the totality of the existences of states of affairs, whatever that might mean? I think the idea is that a fact is the existence of a state of affairs. But why not: a fact is a state of affairs? So far we seem to have got either nowhere at all or else no further than 1. Perhaps the obvious ambiguity or (potential for) confusion is designed to make us attend to definitions, to look carefully for clear understanding.