If you think Legolas did understand that the beast in front was Balrog out of his education by Thranduil, then I will ask you why didn't Aragorn identify the Balrog as what it is?
Throughout the book Aragorn shows a great knowledge about history. He was educated by high-elves that had eye witnessed the war of jewels. When there was some knowledge about Balrogs in Middle-Earth of the late third age than it was stored in Rivendell. But even after the event, when Aragorn had heard the name Balrog from Legolas and Gandalf's acceptance of it, he was not able to name the demon in his retelling to Galadriel. In Lorien it is again Legolas who named the demon a Balrog.
In my view that shows that Aragorn with all his knowledge of the past had never heard of Balrogs before.
Now let us see how you pictured Legolas: Born in the third age as the son of Thranduil a Sindar out of Doriath.
There had been no mention of any fighting Balrog around Doriath at all and the surviving elves of Belerinad did not fight in the war of wrath. So your Thranduil could only have HEARD of Balrogs - on kind of the many demons of the bad old times that had for all knowledge perished all in the last battle of the north.
Not very likely for me that he gave his son a description that was sufficient to know the demon to be a Balrog at once.
In addition, if your read the account of Thranduil in the unfinished tales, that he was during the complete third age concerned about the enemy, that was daunted but not gone for good, it seems very unlikely that an elf in such an mode will beget an child.
So my point in short: Legolas had eyewitnesses a Balrog before he meet the on in Moria. And if so when he was old enough to have been in the wars of the first age, than why not in the Fall of Gondolin? In the old FoG it was not explicit that all the elves of Gondolin were Noldoli. Later this topic shifted some times. So there is a possibility that he was both, a Sinda and an Elf of Gondolin (isn't the house of the Tree really a good name for a Sindarin house?).
And for your mention of Galdor of Gondolin and Galdor of the Havens: If I read the notes concerning Glorfindel of Gondolin and Glorfindel of Rivendell to be the same person, than it say also that Galdor could have been the same person. Galdor survived the FoG, as did Legolas. As a messenger of Cirdan Galdor as a surviving high-elves is likely.
At least you should see that there are some evidence for Legolas being quiet old.
Respectfully
Findegil
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