Elaine Marley from Monkey Island.
Female? Yes
An American? No
Is a star? No (Governor)
Does the character speak to you? No
Go to school? No
Fight? Yes (with undead!)
Anime? No
Linked with shooting games? No
From a video game? Yes
Final Fantasy? No
Human being? Yes (Genie's face is red at this point)
Fight with a sword? Yes
Black haired? No (red/brown)
A princess? No
Red haired? Probably Partially
Scar on face? No
Asian origins? No (Caribbean)
Wear gloves? I don't remember her wearing a pair, no
Pink? No (what was it thinking, Kirby?)
Brother or sister? No
Answer: Aty (Summon Night 3) WRONG!
And I'm not adding Elaine Marley to its database...
Teenager? Don't know
Magical powers? No
Small? No, similar height with everything in the games
Has been president of a country? No
Animal ears? No (Furry warning!)
Pink-haired? No
Fight with monsters? Yes (undead)
A woman? Yes (Didn't you ask that already?)
Ribbon in hair? No
Long hair? Yes
Answer: Karin Koenig (Shadow Hearts 2)
Ride giant robot? No
Blond? No
In love with someone? Probably partially (Sorry Guybrush)
White? Yes
Been into space? No
Ever been shot at? Yes (Lechuck's cannons)
Use a bow? No
Adult? Don't know
Linked with Nintendo? No
Bulgarian? No
Answer: Amy Sorel (Soul Calibur)
I think I stumped it.
Edit: It has Elaine Marley (Monkey Island) in its database, but the parameters doesn't match my choices.