[elbenprincess]

The quote shows that Elrond is especially held in high regard in foresight. He alone is singled out as the most surprising that Cirdan had greater foresight.

“He is not half through yet, and to what he will come in the end not even Elrond can foretell. Not to evil, I think. He may become like a glass filled with a clear light for eyes to see that can.” -LOTR

Only because he said "not even Elrond" means that Galadriel is inferior to him?!?! There could be thousand reasons. I don´t know the context, but maybe they were in Rivendel at this point when gandalf said it and he said it to be poilte and respectful to the lord of the house. The most obvious reason could be, that they dot know Galadriel yet. If he wold say "not even Galadriel" they wold have no idea who he is referring to. Unless the conversation takes place after they went through Lorien, then my argument would be moot.
That tiny bit is hardly the prove of him being superior.

You can not provide any quote which says explicitly that he has the greatest foresight save Cirdan or that he is called by Tolkien "the greatest loremaster"

Elrond symbolises throughout the ancient wisdom, and his House represents Lore – the preservation in reverent memory of all tradition concerning the good, wise, and beautiful. It is not a scene of action but of reflection.-Letter 131

Only because he symbolises ancient wisdom and his hose represents Lore, doesn´t mean that he is the wisest person in ME, that would belong to Cirdan, or even Celeborn, if we can believe Galadriel or that he is the greatest loremaster, cause he is never called "the greatest loremaster of ME" Rivendell just happens to contain the most important artefacts of the past, therefore his house represents lore.
Galadriel would to have acces to that lore, being often in Rivendell and even in Valinor she was eager to learn everything what the Valar cold teach her, wanted to learn even more, one reason she left Aman and then went on lerning with Melian. I dobt her thrist for knowlege vanished.

Where does it even remotely suggest Elrond was under the ban or urged to comeback? In fact the story implies the opposite. Elrond much like Cirdan seemed to have had a special mission to stay in Middle Earth. Elrond to ensure that men could come into their own in the fourth age. Why else would the Valar send Glorfindel to personally aid him if he was still defying their orders?

'The passing 'oversea' to Eressea (an isle within sight of Aman) was permitted to, and indeed urged upon, all Elves remaining in Middle-earth after the downfall of Morgoth in Angband.' Morgoth's Ring

I never said that he was baned, I just thought that he was counciled to go to Aman, but I couldn´t find it, so it is probably not canon.
But in this quote he doesn´t differ, but still Elrond was among the elves who were welcome to go west.

"Elrond much like Cirdan seemed to have had a special mission to stay in Middle Earth."

Sure, Elrond had his purpose and the Valar were happy to have him in ME, but the same could be said of Galadriel.
IMHO you make Elrond too special.
Many elves had their part in overthrowing Sauron. Without Galadriels aid the quest would have failed, the Valar were aware of that and for all her efforts she was pardoned and honoured by the Valar.

Elrond the Half-elven, son of Earendil, maintains a kind
of enchanted sanctuary at Imladris

It says a kind of enchanted sanctary, that gives me the impression, that the "enchanted term" rather refers to Rivendell, but more to the atmosphere that was special, in contrast to the unconquerable borders like it is said when speaking about Galadriels realm.
I don´t get the feeling that it refers to the same power that surrounded and safed Lorien.

Tolkien is here again very ambiguous, he doesn´t go further into detail, it´s not as convincing than the quote regarding Galadriel and Lorien who would only fall if Sauron comes there in person.

Three times Lórien had been assailed from Dol Guldur; but besides the valour of the elven people of that land, the power that dwelt there was too great for any to overcome, unless Sauron had come there himself. Though grievous harm was done to the fair woods on the borders, the assaults were driven back; and when the Shadow passed, Celeborn came forth and led the host of Lórien over Anduin in many boats. They took Dol Guldur, and Galadriel threw down its walls and laid bare its pits, and the forest was cleansed.

No that was the first time, but after that she learned the tongue of birds and the ability to fly, which is a great display of her innate power.

Yes, later on Elwing was still able to fly but only due to the spell Ulmo put over her, that would last forever, or at least as long as he intends.
I don´t think that she was transformed one time and by sheer good fortune was later able to do it all alone. IMHO it was Ulmos gift to her.
Therefore it doesn´t show her innate power, it would have been if she was doing it without Ulmo at all, like Luthien, when she was shapeshifting. But Ulmo could probably make it for every elf possible to turn into a dowe and then back to elf. I don´t think it ever happened again, so that makes her special, the only elf who can fly.

That apart by equal beings, he meant all rational creatures created by Eru from Hobbits to dwarves all the way up to the Valar. I can provide the quote if you want extra proof.

That would be nice.

Even if she didn´t visit or take part in some of the events, she can see everything that she wants with her mirror, how Beren meat Luthien, how Sauron lost his ring and Gondolin, how it was bilt and destroyed.

No she cannot.

Yes she can.

'Many things I can command the Mirror to reveal,' she answered, 'and to some I can show what they desire to see. But the Mirror will also show things unbidden, and those are often stranger and more profitable than things which we wish to behold. What you will see, if you leave the Mirror free to work, I cannot tell. For it shows things that were, and things that are, things that yet may be. But which it is that he sees, even the wisest cannot always tell. Do you wish to look?'

So she has absolutly control over her mirror, she can see in the mirror the past crystal clear, (that is a better tool to lore than everything that is archieved in Rivendel) present anyway, and the future, but there she knows that she has to be careful if she want´s to act on that, cause that again could change the future, cause IMHO the future is variable.
So she is able to see the future, while Elrond it "just" stated to have forsight but never is he, so that no question is left, stated as second to Cirdan regarding forsight.

If you ask for the greatest of the Noldor, then you have quotes which are definite, there is no discussion (actually there is, but that is not the point, Tolkien said so and that´s all what matters).
Regarding Elrond coupled with forsight and greatness in lore, those definite quotes are not existent. The quotes you provided are arguable, cause not one actually states that "Elrond is second to Cirdan in foresight and the greatest loremaster in ME".

I have no problem to be put right, if I missed something.