Alice is often portrayed in fan culture as having an obsession for dolls. In some doujin, she is often depicted making or playing with dolls. It is also widely assumed that she makes dolls of other characters for fun (such as putting on a puppet show with them). This might be somewhat official, as she has at least made dolls representing the Three Mischievous Fairies and used those to mock them in Strange and Bright Nature Deity. She has also used them, in some doujin, like voodoo dolls in a more sadistic manner.
Despite being mistreated often in fan works (or perhaps because of it), Alice is one of the most popular characters.
Likewise in fan works, because of her perceived cold exterior and cowardly true persona, she is frequently depicted as a down-on-her-luck tsundere. In other cases, she's also been depicted as a yandere.
In some comedy-oriented fanworks, she's showed a having love fantasies, or even a yuri relationship with Marisa.