Unless the mod author has actually applied for and received a patent for their mod from the US Patent/Copyright Office (or any other countries patent office equivalent), they don't actually have any legal grounds to make a claim for a copyright infringement if you use their mod without their permission. But that doesn't mean that the policy of the forum that hosts your file can't take it down. Legally, pretty much anything posted on the internet is public, even e-mail. But its still unethical to use someone else's work without their knowledge. Some modders actually post that you can use their stuff without contacting them. For me, I have the opinion that anything I upload can be used by anyone. I believe in the 'open source' ideal and am flattered if somebody wants to use my stuff. The only thing I don't like is if they just copy it verbatim and upload it as their own work. Also, copyrights don't hold internationally unless copyrights were obtained in those other countries as well. I don't believe that Interpol investigates international copyright infringement where the country in question does not recognize the foreign copyright. But in the USA, it can be vigorously pursued.
Patents and trademarks have nothing to do with copyright, and nothing requires you to publish your work or register a copyright; your work receives copyright protection from the instant you created it. With a few strange exceptions like Guatemala, copyright in one country is good everywhere; you do not need to register your copyright in any other country. You may have to register your copyright before suing somebody for infringement, but that's all.
If you use somebody else's mod without permission, you
are committing copyright infringement. The question is whether anybody would bother to act on that infringement. The usual problems seem to be:
* Making a compilation of mods. Many modders don't want their work used in compilations, because the compilation memorializes a version of the mod that will become obsolete. The possibly obsolete and buggy version distributed with the compilation can't be maintained by the original modder and reflects badly on the author. I'll state this one flatly:
Don't even think of publishing a compilation of mods unless you have actually contacted all the authors, received express permission, agreed to abide by conditions they set on their permission, and then actually do so.* Making a change that goes contrary to the intent of the original mod. A mod expresses the intent of its author, and the author may not be willing to countenance changes that go to the intent of the mod. At one extreme, a mod may place something special and elevated into the game, and a change that appears to desecrate that will not be welcomed; for example, any change to
Children of Morrowind that would allow children to be harmed. At the other extreme, the author may have intentionally disregarded compatibility with other mods, and even changing the mod for compatibility would not be permitted.