I am writing a novel and I would like to introduce characters from other published works as time travelers. Is this a bad idea or even legal? Copyright infringement comes to mind... Is there a legal way to use the names of established fictitious characters in my story? I'd hate to make a rookie mistake, but I am a rookie...
That is a bad idea, and yes, it is possible you can be sued for damages.
Other fictional characters are somebody else's work, as a general rule you cannot steal them. Those authors have the right to any profits earned by those characters in any way. They also have the right to control how their characters are portrayed, described, or made to act.
There are some exceptions about characters that are not well-developed, but you will have to talk to a lawyer to see what you can get away with.
If you intend to publish, agents and publishers will reject a work containing some other author's characters. You could self-publish, but then you open yourself up to a lawsuit.
Think of other fictional characters as items of property like a car, you cannot just take it and use it, especially to make money, without the owner's permission.