[Aiwendil]

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?

How do we know he didn't? Merely because he didn't shout about it as Legolas did?

But it is completely possible that, though Aragorn had roughly the same or better education than Legolas, he simply had not been taught precisely what a Balrog looks like. There would have been little need - they were supposed all to have been destroyed.

In my view that shows that Aragorn with all his knowledge of the past had never heard of Balrogs before.

This sounds very unlikely. Never even to have heard of Balrogs would require that he had missed huge portions of the tales of the first age.

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.

Not likely? Perhaps not. But certainly possible, and far more likely than any alternative.

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.

But Legolas is quite explicitly the son of Thranduil: "There was also a strange Elf clad in green and brown, Legolas, a messenger from his father, Thranduil, the King of the Elves of Northern Mirkwood." (LotR II 2).

There is also no indication in UT that Legolas was alive at the time that Oropher moved east. Nor is there any suggestion anywhere that he was the same Legolas as the one from Gondolin. It seems extremely likely that we would have at least some reference - particularly considering that Tolkien clearly thought the matter of Glorfindel's reincarnation so significant, and devoted at least two essays to it. The only piece of evidence you provide to counter this is that Legolas correctly identified the Balrog. That's simply not enough.