The "choice" which Arwen sometimes mentions to Aragorn is the choice she is allowed to make between being mortal (the path of Men) or immortal (the Elven path). She is granted this choice of fate because her father Elrond is half-elven. Although at the time of LotR she is almost 3000 years old, she can choose the mortal path even though she has lived far in excess of a normal mortal life span.
Arwen has two older brothers, the twins Elladan and Elrohir. Galadriel is her maternal grandmother.
The tomb Gimli finds in Moria belongs to Balin who was one of the twelve dwarves who accompanied Bilbo in the Hobbit.
The seeing stone which Saruman uses is one of the seven Palantir stones. These were made in Valinor by the elves and brought to Middle Earth by Elendil before the sinking of Numenor.
Orthanc, the tower of Isengard was originally built by the Dunedain of Gondor from four pillars of unbreakable black rock.The tower stands 500 feet high.