Unfortunately, it is very unlikely that there would be any anime, manga or video games left. Exsilium on its own is meant as a sort of prison belonging to the United Earth, so it would be difficult to get the newest technology (like a gaming console) there. The United Earth may have some, outside of the island, though their trustworthiness would be up for debate.

They do have televisions, but no channels that are not United Earth-approved viewing. So, propaganda and heavily censored news is the most likely thing to find there. It is possible that she could maybe dig up some DVDs or VHS in old basement storages of some run-down/abandoned buildings in the City, though! Or others could, if she asked them to find some for her. :)

Also, all questions are a-okay :3!