Departure of the Galadhrim

[Findegil]

It is true that Sauron drove the Elves north in Mirkwood, but Lorien was already inhabited by the woodelves long before that time. Sure, the contact between the Mirkwood-Elves and the Lorien-Elves before the former moved north was close, so that there might have been some of the Mirkwood-Elves going to Lorien instead of north. But I don't think that this happend enough to make the move to Greenwood in the fourth age a return home.

Respectfuly
Findegil

[Galadriel55]

I have another question in mind: what happened to the Elves of Rivendell and why couldn't the Galadhrim go there? As we know, Elrond had Vilya, and although he didn't use it as much as Galadriel used Nenya, his absense was felt keenly by his Elves. Why couldn't the two "collapsed civilizations" unite? They have a lot in common as well.
As for why the Galadhrim left so quickly, maybe they understood that after Galadriel's departure they will not be able to live regular "Galadhrim lives". They faced two major changes: Galadriel leaving and them leaving Lothlorien. Maybe they just didn't want to stretch the tie between them.
Moreover, it says that eventually all the Elves will leave ME. How and why? Mirkwood Elves aren't bothered by the memory of Valinor. Legolas wanted to leave only because he heard the Sea, but not all Mirkwood Elves did, so why should they leave?

[Inziladun]

Originally Posted by Galadriel55

I have another question in mind: what happened to the Elves of Rivendell and why couldn't the Galadhrim go there? As we know, Elrond had Vilya, and although he didn't use it as much as Galadriel used Nenya, his absense was felt keenly by his Elves. Why couldn't the two "collapsed civilizations" unite? They have a lot in common as well.

A remnant of the people of Rivendell possibly did stay there after Elrond's departure, but I think there's room for debate on that subject (see the above comments).
Even if some did remain in Imladris after Elrond left though, they really didn't have that much in common with the Galadhrim. The former were Noldor, the latter Silvan, with a different culture. I can't really see the Lórien folk actively seeking out Rivendell, when there were other Elves more closely akin and much nearer at hand in Mirkwood.

Originally Posted by Galadriel55

Moreover, it says that eventually all the Elves will leave ME. How and why? Mirkwood Elves aren't bothered by the memory of Valinor. Legolas wanted to leave only because he heard the Sea, but not all Mirkwood Elves did, so why should they leave?

The leaving of the Elves was tied to the arrival of the Age of Men, in which the other 'speaking peoples' of Middle-earth gave way for Men's dominance. Additionally, I think all Elves, even the Moriquendi in Mirkwood, would sooner or later have felt the call of the Sea. Legolas was merely hit by it earlier because of his encounter with the seagulls. It seems to me that all Elves really belonged in the Undying Lands, a place where the environment was perfectly suited to their own "immortal" nature.

[Galin]

Still Tolkien refers to the Lingerers, Elves who remained so long in Middle-earth that they faded in the body.

How many and how long they remained... I'm not sure. The latest version of the poem The Trees of Cortirion suggests these Lingerers in my opinion.