Galadriel's power

[Inziladun]

Though Galadriel was probaby the most powerful of the Eldar remaining in Middle-earth in the Third Age, I can't put her on an equal footing with Sauron, even bereft of his Ring.

'What power still remains lies with us, here in Imladris, or with Círdan at the Havens, or in Lórien. But have they the strength, have we here the strength to to withstand the Enemy, the coming of Sauron at the last, when all else is overthrown?'
'I have not the strength,' said Elrond; 'neither have they.'

Thus spoke Elrond at the Council. That seems pretty definitive to me, but I think Galadriel herself gave a clue as to how she would fare against Sauron.

'Do you not see now wherefore your coming is to us as the footstep of Doom? For if you fail, then we are laid bare to the Enemy.'

By 'if you fail', she doesn't specify 'if Sauron regains the Ring', only that if the Ring is not destroyed then he will be victorious. I take from that, and Elrond's words, that Galadriel could not resist Sauron indefinitely regardless of whether he held the One.
She could easily have known how many times Frodo had used the Ring; he had given a full account of events at the Council of Elrond, and she had obviously been informed of what was said there.

Her perception of Sauron's mind concerning the Elves, but not the reverse, I see as possibly a statement on the relationship between Good and Evil; that the Good can understand Evil more easily than Evil can understand Good.

'Well, let folly be our cloak, a veil before the eyes of the Enemy! For he is very wise, and weighs all things to a nicety in the scales of his malice. But the only measure that he knows is desire, desire for power; and so he judges all hearts. Into his heart the thought will not enter that any should refuse it, that having the Ring we may seek to destroy it. If we seek this we shall put him out of reckoning'.

FOTR The Council of Elrond

A curious blindness that Evil has, exploitable by the Good.

Her statement that she wished the Ring had not been wrought or had remained lost could simply mean that she somewhat regretted having made Lothlórien the earthly paradise that it was; for she had come to love it, and knew that Sauron being aware the Ring had been found had fully awakened him, and Lórien was near to its doom no matter the result of Frodo's errand.