Heroic BSOD: In episode 11, she temporarily "forgets" how to speak Japanese because she is afraid Shino no longer likes her due to becoming Japanized.
The Ingenue: She looks like a child in any way possible, physically and mentally. A little point in Episode 8: she still needs Shinobu to take her to the bathroom in midnight!
Nice Girl: Sweet, kind-hearted, caring, friendly, and compassionate. Heck, she even helps cheer Shino up when she found out that Shino didn't do that well in the math test.
Older Than She Looks: Alice is roughly around the same age as Shinobu, yet her petite size makes her pass her as an elementary or middle school student. You're right, Alice, an English girl, is small by Japanese standards.
Multiethnic Name: Hers is an unusual form of this trope, as she lampshaded. The name was deliberately chosen so that it taken as completely different names in different languages. The English use of this name has Armenian roots, while the Japanese use of the same name is a Chinese loanword, meaning "adorable." (Yes, the "Karen" in Zettai Karen Children)
Neologizer: She frequently speaks in broken Japanese and custom words like "Ohayou goshaimashu" (Good Myowrning). Her class then copied it from her, thinking it was cute.
Nice Girl: The reason why many of her classmates were giving her snacks.