Is there any particular order the categories should go in?We generally favour ordering the categories alphabetically, though it's OK to put the Trope Namer's category first. Also, if a trope is primarily associated with one medium, that medium should naturally go at the top. However, in all cases, Real Life always goes last, and Other goes before Real Life but after everything else. If you see an category in the wrong place, go ahead and move it.
What category do animated films go in?They get their own category, namely Films — Animation.
Why do animated films get their own category?To avoid confusion over whether they belong under Films or Western Animation (or Films or Anime & Manga, for Japanese animated films). No, that's not how it works with the namespaces.
Couldn't you solve that problem by having a unified Films category and a unified Television category? Alternately, couldn't you solve that problem by having a unified Live-Action category and a unified Animation category?The Western Animation, Live-Action TV, and Films categories are often very large already. Combining them into two larger categories would make it more difficult to find specific examples. Also, trying to do the combination might lead to holy war between people who think the film vs. television distinction is more important and people who think the live-action vs. animation distinction is more important. It's much simpler just to make both distinctions.
Why is Anime & Manga its own category, rather than being combined with the Animated Television and Comic Books categories?There are several reasons for this:
Where should examples from William Shakespeare go?If there's a Poetry category, list his poems there. If not, they can be listed under Literature, or you can make a Poetry section. His plays are always listed under Theatre; if you see one listed under Literature, that is an error, and it should be moved.