To some extent this is self-explanatory, since all the references are, as far as I can ensure, genuine. But of course it isn't really a scholarly analysis of Eliot and Shakespeare, and its readers are not, mostly, academics (any more than I am) whose backgrounds can be assumed.
"The Chair she sat in, like a burnished throne" is indeed the first line of the second section ("A Game of Chess") of The Waste Land by T.S.Eliot.
"April is the cruellest month" is the first line of the whole poem.
"Consider Phlebas" is a phrase in the fourth section, and the title of a book by Iain M. Banks.
"Seven Types of Ambiguity" by William Empson has an analysis of the passage from Eliot.
The part of the piece that examines the "parallels between Enobarbus and Tiresias" is intended to be genuine - but it is still a pastiche.
Two references: "fall apart" is from Yeats, "The Second Coming"; "seat of the scornful" is from Psalm 1.
Everything else can be found in Shakespeare ("Hamlet", "The Tempest", "Antony and Cleopatra") and Eliot ("Prufrock", "Four Quartets", and "The Waste Land").