Are these things written in the Fourth Age, being the Age after the books, or are they from the previous Fourth Age (i.e. six Ages ago)? Are they really prophecy? More likely, they are supposed to be histories of Rand's Age, written during the Age which will start with the end of the last book. Thus, they are not prophetic in the technical sense - they are supposedly written after the fact - but they are prophetic to us, because we don't yet know the end of the story.

From The Eye of the World

[TEOTW: Prologue, Dragonmount, xv]

And it came to pass in those days, as it had come before and would come again, that the Dark lay heavy on the land and weighed down the hearts of men, and the green things failed, and hope died. And men cried out to the Creator, saying, O Light of the Heavens, Light of the World, let the Promised One be born of the mountain, according to the prophecies, as he was in ages past and will be in ages to come. Let the Prince of the Morning sing to the land that green things will grow and the valleys give forth lambs. Let the arm of the Lord of the Dawn shelter us from the Dark, and the great sword of justice defend us. Let the Dragon ride again on the winds of time.

(From Charal Drianaan te Calamon, The Cycle of the Dragon. Author unknown, the Fourth Age)

The "Dark laying heavy on the land" and the failing of plants refer to the two bouts of (Shadow-caused) bad weather we've had in the series thus far, which have caused crops to get messed up: the super-long winter in TEOTW, and the recent hot spell. The reference about singing and fertility

could

mean that the Song will be found, but it could just as well be meant figuratively.

From The Dragon Reborn

[TDR: End Prophecy]

And it was written that no hand but his should wield the Sword held in the Stone, but he did draw it out, like fire in his hand, and his glory did burn the world. Thus did it begin. Thus do we sing his Rebirth. Thus do we sing the beginning.

Fulfilled--Rand took out the Sword in the Stone.

From The Shadow Rising

[TSR: End Prophecy]

And when the blood was sprinkled on ground where nothing could grow, the Children of the Dragon did spring up, the People of the Dragon, armed to dance with death. And he did call them forth from the wasted land, and they did shake the world with battle.

(from The Wheel of Time by Sulamein so Bhagad, Chief Historian at the Court of the Sun, the Fourth Age.)

Fulfilled--Rand brought the Aiel out of the Waste to do battle.

From The Fires of Heaven

[TFOH: End Prophecy]

And the Glory of the Light did shine upon him.
And the Peace of the Light did he give men.
Binding nations to him. Making one of many.
Yet the shards of hearts did give wounds.
And what was once did come again
--in fire and in storm
splitting all in twain.
For his peace...
--for his peace...
...was the peace...
...was the peace...
...of the sword.
And the Glory of the Light did shine upon him.

(from Glory of the Dragon, composed by Meane sol Ahell, the Fourth Age)

General prophecy. Not too informative.

From Lord of Chaos

[LOC: Header Prophecy]

The lions sing and the hills take flight.
The moon by day, and the sun by night.
Blind woman, deaf man, jackdaw fool.
Let the Lord of Chaos rule.

(chant from a children's game heard in Great Aravalon, the Fourth Age)

Your guess is as good as mine as to whether this is actually prophecy/historical or not.

From Crossroads of Twilight

[COT: End Prophecy]

We rode on the winds of the rising storm,
We ran to the sounds of the thunder.
We danced among the lightning bolts,
and tore the world asunder.

(Anonymous fragment of a poem believed written near the end of the previous Age, known by some as the Third Age. Sometimes attributed to the Dragon Reborn.)

Technically I suppose this shouldn't be in the "Fourth Age" section since it was written in the Third Age, but this fit best, as it is written from a historical perspective rather than a prophetic one. Seems to be a reference to the Asha'man, or maybe all channelers, and the prophesied Second Breaking of the world. If referring specifically to the Asha'man, could be related to Elaida's Foretelling of the Black Tower rent in fire and blood.