Here's my best textual analysis for clues, edited with feedback:
AN ANCESTOR OF YOUR BLOOD FOUND THEIR CURSE IN HERE
Guessing this refers to Ignotus Peverell receiving the Cloak. This is no mere dream, this is Death's Realm, or a dream of Death's Realm.
Above it, many hundreds of meters above, translucent figures danced and thrashed in the sky, running away from the center of the city, flashing their ectoplasmic cauls not unlike ghostly fireflies. It was a mesmerizing, albeit terrifying sight.
More evidence that this is Death's Realm, or a reflection of it.
NONE THE LESS, MY BEARING REMAINS SMALL AND SHALLOW AS IT WAS MANDATED BY THE ANCIENT'S GREAT TEN THINGS
The ancients did something to impair the Guardians' ability to interfere. Or whatever this spirit is.
AND FORTHWITH YOUR FOCUS ABANDONS IT SHOULD YOU SURVIVE.
Harry will forget if he survives?
MY PURPOSE IS TO BRING YOU VICTORY, EITHER IN BLADED FORM OR AS SHADES OF MYRIAD COLOR, THAT YOU NEVER SEE.
Bladed form might be an Excalibur reference.
BUT, IN GENEROUS-FREEDOM, THIS HAS NOT REMAINED IN THE BRAGGART'S AMUSING PAPYRUS LEAVES WITH SYMBOLS OF FATED MEANING. TO THE UTTERMOST SADNESS OF EVERYTHING BREATHING, YOU ARE NOW PLANTED FIRMLY IN THE SOILS OF THIS WHISPERING PHANTASM OF A PAST TRAGEDY. I CURSE THE DEVIOUS ARCHITECT OF YOUR FATE; THOUGH I LACK THE ARMED CAPACITY TO SEE MY FEY WORDS BURNED INTO THE STONE OF SUBLIMATION.
Victory is no longer in the cards?
What's the past tragedy?
AT FOREVER'S CLOSURE OF THE RISING SUN
The rune of dusk?
YOU MUST LEARN TO MASTER THE WINDS MADE INTO TREES
I'm guessing this is 'learn to master the trees made into wands', ie the Roman Wand Wood.
FROM THOSE WHO BEAR THE MARKS OF PHOENIXES
The old members of the Order of the Phoenix.
THERE ARE ELDERS WHO WALK IN ROBES OF GLIMMERING STARS, AND GROW THEIR BRISTLES DOWN, AND THEY WIELD LINES OF PASSION, POWER, VIVACITY, MADNESS, AND OTHER COUNTLESS CONJECTURAL EXTRACTIONS, AND YOURS IS THE DUTY OF VINDICTIVE, PAINSTAKING APPLICATION AT THEIR FEET.
'Grow their bristles down' means bearded. Robes of glimmering stars could be literal or figurative, the stars being a metaphor for fate or power. Could be a reference to House-related spirits or the founders.
ARE YOU IN COMMAND OF YOUR EARS AND EYES, BORN OF VESSELS? UNWISE TO FORGO THE PRIME PENTAGON OF EFFLUVIAL RADARS, ESPECIALLY IN A DIRE LOCUS.
Clear enough. It's unwise not to pay attention to your five senses when in danger. 'Born of vessels' likely means Potter.
NO CHAOS-DISPELLING PATTERNS EXIST HERE. YOUR HISTORY UNWEAVES IN EVERY SECOND, ITS STRINGS UNLOOPING, UNTETHERING; EVERY STRING MEANS FOOTSTEPS LOST ON THE WAY, AND EVERY FOOTSTEP IS CERTAINTY OF TRUTHS.
Suggestive of a time travel paradox, I think.
BUT THEIR TWILIGHT COMES SOON, AND WHETHER THAT HAUNTED YET GLORIOUS ERA COMES BY THE WROTH CHAINS YOU WROUGHT INTO THE HANDS OF SKYLIGHT WITH EFFORT AND GRACE, OR BY THE MANY HUNDRED ASPIRANTS WHO FOLLOW YOUR PATH
Harry's fate is to end the gods - Death included - by mastery of astrology or by leaving teachings to others who follow after him?
I AM FREE NOW AND FOREVER, OUTSIDE OF FOREVER, AND BOUNDED BY NOTHING. CALL UPON ME WITH THE SIGIL SHOULD YOU CHANGE THAT.
The spirit is banished outside of reality, and would like to be rescued if Harry can find a way, or if Harry manages to avoid creating him in the future, perhaps.
almost like an ouroboros made of triangles put on scales, with a counterpart in the form of an overflowing cup that steadily poured away lines of stars into a pool of water underneath the scales. And in the waters, resting deep within, shone a golden sword.
Not sure if scales like a lizard or scales like weighing scales. I'm guessing the former. Triangles put on scales doesn't make much sense, but scales in general makes me think of the basilisk. The rest of it looks to me like a reference to the Grail and Excalibur, two core pieces of Arthurian myth. It might be a hint that Excalibur rests beneath the lake, beyond or guarded by the basilisk?
[X] Heed the Spirit's Advice
[X] Seek Death 
