I don't really blame Galadriel for trying to vaunt her powers in the face of everyone else. After all, she was the last one of the direct line of the House of Finwë, which, in itself, is an honor. She was also the last Elf (or one of the last Elves) who had seen the light of Aman, thus, making her more powerful than the rest.
Even in Aman, Galadriel had always been proud of her abilities. I think it was a Noldo thing! I'm sure that people told her that she was the greatest of the Noldor (except for Fëanor, but he's a way different topic), and that could have gone slightly to her head. It says in the Silmarillion that all of the descendants of Finwë were proud and masterful, and that would definitely describe Galadriel.
I think that the reason time seems to freeze in Lothlorien is that Galadriel didn't want her realm to fall, like the realms of so many of her kin. She saw Nargothrond fall, the realm of her brother. She saw Gondolin fall, the realm of her cousin, Turgon. She saw Doriath fall, the realm of one of her greatest teachers and her kinsman. And finally, she saw Lindon fall, along with the last of the High Kings. She didn't want the same thing to happen to her and her kingdom, so that was why Celeborn was probably the one who did all the traveling. I don't recall any mention of Galadriel ever leaving Lothlorien for anything, except for Aragorn and Arwen's wedding and a few visits to Rivendell in the early Third Age.
She was so protective of her kingdom because she wanted it to resemble Aman, and Doriath. She probably learned how to guard it from Melian, who practically was the Maia of Guarding, and after Doriath's fall, Galadriel was the last "heir" of Melian alive. She probably wanted her kingdom to be a testament to her teacher.
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But Melkor also was there, and he came to the house of Fëanor, and there he slew Finwë King of the Noldor before his doors, and spilled the first blood in the Blessed Realm; for Finwë alone had not fled from the horror of the Dark.
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