Are Aragorn and Arwen an item?

They really are an item. আরো to their story is written in 'Return of the King' and in Appendix A, where আপনি get a lot of information on their backstory.
Galadriel is indeed Arwens grandmother. Her daughter married Elrond and became three children, Arwen being the youngest of them. But she went to Valinor long before the Lord of the Rings started.

YES THEY'RE AN ITEM! IS THAT NOT OBVIOUS?

Yes. Their relationship is very complex, and is actually mentioned আরো in the চলচ্চিত্র than the books. I'll give আপনি a quick run-through of their relationship.
First thing to know is Arwen is one of the half-elven. This means she has mortal blood. Her great-grandmother (on her father's side) Idril married a mortal man called Tuor and her great-great-grandmother (also on her father's side) Luthien married a mortal man called Beren.
This gives Arwen some interesting options. As she has mortal blood, she can make the choice to 'give-up' her status as an Elf and live as a human. Now, this wouldn't mean she would suddenly lose her pointed ears, অথবা the ethereal beauty associated with the Elves. It means she would have the ability to die as a human would.
Death is what really separates Humans and Elves. For humans, they live - on average - between 50 and 80 years and then die. Nobody knows what happens to a human's soul after death. However, Elves are immortal in that their souls are completely bound to the living world. An elf can be killed (they don't die of natural causes), but it's soul will linger, and eventually they will be reborn into a new body identical to the old one.
So, Arwen, like all other half-elven, has the choice on whether to become mortal and die, অথবা become elven and live forever, and this is her choice to make.
Now, it should be mentioned that her siblings and her father's family have had to (or will have too soon) make this choice. Out of the family members who have this choice, four have chosen to be elves, one has chosen to be mortal, two have not decided and two were killed before they could make the choice. The one who chose to become mortal was Arwen's uncle, Elros, who was the twin brother of Elrond (Arwen's father). Elros chose to become mortal and became a king of mortals. Now this kingdom flourished for about two thousand years (Elros had long passed away দ্বারা this point) but the people of the kingdom became corrupted দ্বারা Sauron and turned against the Gods themselves. These mortals then broke every rule set before them and the Gods had no choice but to decimate them and the while kingdom. The only survivors were the few who still were loyal to the Gods. These people set up the new kingdoms of Anor and Gondor, which is where Aragorn comes into the picture.

Aragorn and Arwen are an item and at they end it is ব্যক্ত that they married and Aragorn became King of Gondor. Galadriel is Arwen's grandmother through Celebrian, Arwen's mother.

YES! They just moved it to the appendix