That used adverbially is wholly inexcusable. "He was that sick" could only be tolerated if an ellipsis such as "he was (to) that (degree) sick," could be supposed, but this is more than can be done; and the expression is therefore regarded as an unpardonable vulgarism. Compare as, that (p. 22).
that there: An illiterate expression commonly used with the mistaken idea that the use of "there" adds emphasis to what follows, as, "That there man." Say, rather, "That man there" or simply, and preferably "That man."
that, who: Discriminate carefully between these words. That implies restriction; who generally denotes coordination. As an illustration of this distinction, Alfred Ayres says ("The Verbalist," p. 202), "'I met the boatman who took me across the ferry.' If who is the proper word here, the meaning is 'I met the boatman, and he took me across the ferry,' it being supposed that the boatman is known and definite. But if there be several boatmen, and I wish to indicate one in particular, by the circumstance that he had taken me across the ferry, I should use that." That ought, therefore, to be preferred to who or which whenever an antecedent not otherwise limited is to be restricted by the relative clause.
that's him: No, "that's he"—this is correct.
the: Before titles of honor, such as Reverend, Honorable, the definite article (though now frequently