[Willemijn]

No it's not, because the statement was before Gil-galad died. Galadriel never had the position that Gil-galad as King. Even after Gil-galad's death the most influential person amongst the elves would be Elrond.

The quote says that she was

"the mightiest and fairest of all the Elves that remained in Middle-Earth" (after the death of Gil-Galad)

So before the death of Gil Galad she wasn´t the mightiest in political power, that was of course the king (the fairest part is strange, cause I don´t think Gil Galad was fairer than her, but who knows).

No she doesn't. Her displays of magic are not above those of Elwing, Feanor, Elrond or arguably her brother Luthien.

Well, the ability to have a magic mirror where she is able to see past, present and future, the fact that she destroyed Dol Goldur

They took Dol Guldur, and Galadriel threw down its walls and laid bare its pits, and the forest was cleansed.

, that she was able to make the star glass, to keep Lorien safe from danger with her power and to make that land the most beautiful part in ME, without stain, her sending the fog to Eorls troup and so on is for me above that of Elwing turning into a bird (which she only was able to due to Ulmos help I´m sure! I know she learned the language of birds and seeminly transformed herself later on alone, but for me the enchantment from Ulmo still lies upon her) or Elrond making a flood.

With Luthien and Feanor it´s clear that they are magically superiour to her but with Finrod I disagree, sure disguising himself and his companions or singing a song of power and almost winning against Sauron is impressive, but evidence is that Galadriel is greater than him so that puts her above him.

Earedil was called the mightiest of the Half-Elven, which means he was more powerful than Elrond an equal of Galadriel at the very least.

Only because Earendil was mightier than Eldond doesn´t put him above Galadriel, only because you think that Galadriel is only equal or even inferiour to Elrond.