The trees thing is as yet unfulfilled, but the broken crown refers to Faile and her relationship to the queen of Saldaea. In the prologue to PoD, it is stated that if Tenobia dies without issue, Davram Bashere or his heir will succeed her. Faile is his heir, and Bashere himself refers to the Broken Crown when he accuses Perrin of marrying Faile for her titles. The implication is that there was some controversy over who should have inherited the crown of Saldaea, perhaps with Bashere refusing to concentrate on his military duties or some other outcome, and that his family has as strong a claim as the royal family. It seems significant for Perrin as his marriage to Faile has him three heartbeats away from that same crown.

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The Prophecy of Rhuidean foretold that Rand would pour out the blood of the Aiel like water on sand, and that same metaphor was used to describe one of his early workings of the Power in tGH. The black rock is as you say, and the white hot iron and begger's staff have yet to be resolved.