The story is known only through Hávamál, a piece of poetry from the poetic Edda, in which it takes up two stanzas. The relevant here is stanza 138:
Veit ek, at ek hekk
vindga meiði á
nætr allar níu,
ok gefinn Óðni,
sjalfr sjalfum mér,
á þeim meiði,
er manngi veit
hvers af rótum renn.
I think it's safe to say that at least the Norns knew the language of the runes from the Völuspá:
There stands an ash called Yggdrasil,
A mighty tree showered in white hail.
From there come the dews that fall in the valleys.
It stands evergreen above Urd’s Well.
From there come maidens, very wise,
Three from the lake that stands beneath the ...
Some Norse myths are depicted on rune stones or other objects, but I am not aware of anything like that for Yggdrasil. The oldest depiction I know of is an illustration in a 17th century manuscript of Snorri's Edda (can be seen here), so it's quite a bit younger than the actual myth. Snorri's Edda is also the source that gives most details of the tree, even ...
I don't know if the leaves had any magical properties, but apparently it dripped honey:
I know an ash-tree stands called Yggdrasill,
a high tree, soaked with shining loam;
from there come the dews which fall in the valley,
ever green, it stands over the well of fate. (Vsp. 19, Larrington)
The dew that falls from it on to the earth, this is what people call ...
There's also an interesting Eddic poem called Sigrdrífumál in which the valkyrie Sigrdrifa instructs the hero Sigurd in runic magic. (Sigrdrifa, Victory-Bringer, is often identified with Brynhild, so it is possible she learned the runes from Odin, her former patron. The poem does not mention this, however.)
Yggdrasil doesn't seem to have an origin; in the Prose Edda, which is a compendium of Norse myth, we get a description of the various beings that live in and around the tree, and how its three roots extend across the cosmos, but nothing about how it came to be. (You can find a pdf of Faulkes' translation here, or an older one on this page.)
It doesn't ...
I recently read Neil Gaiman's Norse Mythology. Although he's probably not considered the top authority on Norse Mythology, he did study the important works of Sturluson.
Here's a quote right form the beginning, to add to what you already said about Muspelheim and Niflheim (and this quote is on the back cover):
Before the beginning there was nothing - no ...
To the ancient Celts, certain trees, especially the oak, ash and thorn, held special significance.
To the Celts, Druids and many other peoples of the old world, certain trees held special significance as a fuel for heat, cooking, building materials and weaponry. In addition to this however, many woods also provided a powerful spiritual presence. The ...
Well, I know that with the Ancient Celts the tree of life was a big thing to their culture, to the extent they believed they were trees, or came from trees. They saw them as the symbol for balance, and would leave a big tree to stay on their land because of their beliefs that they were magic (as they provided a multitude of uses such as food and medicine); ...
Not sure if this is what you're looking for, but it looked promising.
"Odinn and His Cosmic Cross" (pdf)
The term used is sjalsforn (self-sacrifice). "...sjálfsfórn contains metaphysical concepts found in religions across the globe..."
"This work will broaden the discussion ...
In Völuspa 2, when describing how she was fostered by giants in the beginning of time, the völva says that she remembers "mjötvið mæran, fyr mold neðan" (the glorious measuring-tree in the earth below). This probably means that the world tree sprang from the ground as the world was created.