When once you have tasted flight, you will forever walk the earth with your eyes turned skyward, for there you have been, and there you will always long to return. (Leonardo da Vinci)
Should "When" not be there, because "once" itself will be able to lead a subordinate clause?
Should there be "on" between "walk" and "the earth"?
Should "there" be "where" instead, so "where you have been, and where you will always long to return" becomes the object of prep. "for"?
Briefly, no.
I have been unable to locate the original of this translation, or its date; but† it is written in a fairly old-fashioned formal register in which the use of once to mean “when once”, “when for the first time” would be jarringly colloquial.
Walk the earth (the roads, the fields, &c) is an old but not entirely obsolete expression in which the sense is “walk about in/on”. We still say “when dinosaurs roamed the earth”.
For here is not the preposition but the conjuction, meaning “because”—“because you have been there and you will always long to return there.“
† SUPPLEMENTAL:
It appears virtually certain that this “quotation” is a 20th-century invention. Nobody has been able to locate it in any of Leonardo’s known writings, and it is certainly not in the Flight of Birds codex to which it is sometimes attributed. For details of one search see Wikiquote.
It's non-standard / archaic / poetic usage to start such a sentence with the (optional) word once. As in...
Once bitten, twice shy.
Equally, walk the earth is somewhat "poetic", but it's still perfectly current to say, for example,...
I've been out walking the streets all afternoon, looking for my lost cat.
As to the third point, there is perfectly valid. But note that again it's stylised/poetic. Idiomatically, native speakers would normally say...
...you will always long to return there
TL;DR: It's all grammatically "valid", but don't copy any of it. People will think you're a bad Victorian poet!
