Mickey is trademarked. Old Mickey Mouse movies, like Steamboat Willie, will be free to copy and distribute but I don’t think other people will be permitted to produce new works starting Mickey Mouse.
It’s a bit of a legal gray area. I don’t think anyone has settled the question about whether trademarking characters runs afoul of the constitutional prohibition on perpetual copyright.
Based on how much money Disney has put into absorbing every trademarked franchise ever (Marvel, Star Wars, etc.), it seems like they’re willing to bet on those trademarks being enforceable.
Sherlock Holmes is also a grey area. My understanding is that the original Sherlock Holmes stories written by Conan Doyle are public domain, but not Holmes material written at a later date [1]
Yes, they can and they have. You can search for articles on Disney suing people in places like China for selling or featuring images of Mickey Mouse (or lookalikes).
A perverse effect (I think) of trademarks is that the owner of a trademark has to sue to protect it from infringement: otherwise, it becomes a common mark, not a trademark, and is usable by anybody.
