'They are'. But I'd lose the 'illnesses in the second sentence, and repeat it in the third:
There are illnesses we cannot treat - fatal diseases. Examples of such illnesses are AIDS and cancer.
When working on this text, you may find it interesting to know that there's a strong collocation between 'terminal' and 'illness'. One talks about 'a fatal wound' but 'a terminal illness'. 'Fatal disease' is perfectly acceptable, but I think more native speakers would speak of such a disease as 'terminal'.
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