Your question shows that you are a critical thinker, unwilling to content yourself with superficial explanations. However, I believe cataphora is not what you think it is. Cataphora is uncommon in English (and in other languages I know). A typical instance of cataphora:
A typical amphora is this: an oblong, disposable vessel used for storing foodstuffs.
The reader cannot understand what this refers to until the 'postcedent' follows: it 'dangles in the air' until you read on. That is essential to cataphora. If you already know what the pronoun refers to by the time you read it, or if the reference doesn't become any clearer in the following sentence, then it isn't cataphoric. Notice how a colon has a very similar function: it indicates that you cannot properly understand the main clause without reading the explanation or enumeration after the colon.
I like those students who give me candy.
Here those clearly refers forward to who give me candy. Until you read the who clause, the word those hangs in the air.
In essence, there is a different between semantic reference and syntactic reference. In the first example you give, there is semantic reference, i.e. the pronoun that refers to the same entity in the real world as the death of... does. However, that isn't enough for there to be cataphora or any kind of syntactic reference. Consider this example:
The book Bridehead Revisited was written by Evelyn Waugh—a man, despite the feminine-sounding name.
The word man refers to the same entity in the real world as Evelyn Waugh. But that is semantic reference, not syntactic reference, and so it has nothing to do with anaphora or cataphora.
Your first example is a simple case of anaphora.
In your second example, that is a conjunction: it merely introduces a subordinate clause without having a specific reference itself. This use of that is probably a remnant of an older (possibly Proto-Indo-European) construction with an antecedent, as in one reason is [the fact] that..., he told me [the fact] that..., they ordained [the ordinance] that... In that older construction, it was anaphoric.
Your third that is a relative pronoun. Relative pronouns are (almost) always tied to antecedents. In this case, that specifically refers back to places, so it is anaphoric, as are almost all relative pronouns.
A case could be made that relative pronouns like what can be cataphoric. No explicit antecedent is in evidence:
What she told me is true.
Perhaps it could be argued that what she told me refers cataphorically to the (omitted) subject of the main clause, as in what she told me: [it] is true! But you'd have to investigate the origin of this construction.
