As the title says, I'm not sure of the difference between 災難 and 災い. Both seem to be mainly used for "personal" disasters (as opposed to 災害). There is a GOO Thesaurus page, but it doesn't really help me here. It does indicate 犬にかまれるとはとんだ災難だ is natural but にかまれるとはとんだ災いだ is odd. Is there a reason for this?
Another more minor question: while the thesaurus indicates only 難 is used for Xの constructions for defining a type of disaster, I see many example sentences of the form 難を避けた, 難を免れた, and so on. Is "難を(escape-like word)" another specific pattern that is exclusive to 難? And are the Xの難 and 難をescape patterns the only way 難 is used?