Well, the Sil says that he is a kinsman of Thingol- who thought himself Lord of
Beleriand. That's pretty impressive.
To a lesser degree, he implies that he is related to Thranduil- who is still
high royalty.
or, he could be related to Lenwe or Denethor, the leaders of the Nandor.
'His land' is Lothlorien, since he rules over it and accounts himself as its
guardian. Even if he didn't grow up there , that's his land. So when Galadriel
left, Celborn still had Lorien, she had nothing. When Arwen died, we somehow
know Celeborn is has sailed West or died by the death of the elanor and
niphredil- that forest is his domain, with or without Galadriel. Without
Celeborn and the Galadhirim, the forest is dead. Mighty as she is, she cannot
understand the love Wood-Elves have for trees and forests, since she aches for
the Sea. Those loves are equal but cannot
coexist.
There is but one task remaining in Arda-we,the Dragons of Valinor will make it happen.