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Her real name is unknown.
She did not participate in the Holy Grail War of her own will, she simply found herself as one of the Masters before she knew it. She is your opponent in the third round.
She is a young girl around eight years old with a cute girlish appearance. Her personality matches her appearance; innocent and weak. Although she possesses great magic which was put together for her by SE.RA.PH, her magus survival instinct is weaker than the protagonist’s.
Until encountering Alice, the protagonist had only fought against stronger opponents, but now the protagonist faces a Master that is weaker than them, and also friendly.
Her true identity is a net-ghost that wanders around the cyber world.
Alice has no physical body.
She wanders through SE.RA.PH as though in a dream, coming across new places to play.
“Well, I saw a lot of people I didn’t know get together, and it looked like fun.”
This little girl had played alone for a long, long time. She joined in on this life-or-death competition because she was lonely.
The Holy Grail War is a cruel competition, and she fails to understand the importance or need to steal the lives of others.

Before Alice passed away, she lived in England.
In an air raid at the end of World War II she was gravely injured and her remaining days were said to be numbered. However it was discovered that she had magic circuits, and after that she was kept alive as-is for research purposes. After a few years of experiencing continual pain and suffering, her physical body finally died. However her mind that was connected to the net remains, and she continues to live as a cyber magus.
She had run from a reality which held only pain for her into a cyber “Dream World.”
As she wandered around the network she came across Moon Cell, and then made a contract with the only friend she’d ever had; Caster.
After formally becoming a Master, she did not immediately participate in the Holy Grail War, she just gazed upon the world of SE.RA.PH. Occasionally she would find another Master who she thought was similar to herself, and in order to speak with him/her she would descend upon the grounds of the final tournament.
…However, upon entering the final tournament one cannot help but fight.
Like this, the young girl who was chased from reality was once again embroiled in conflict in the cyber world.
The innocent Alice does not understand what killing is or how cruel a life-or-death battle can be.
In spite of this, in order to forget the sad memories of the reality from which she ran away, she indistinctly embraces a desire to play with someone.

Fate/EXTRA Material: Encyclopedia of Fate/EXTRA