So when is it okay to enforce your copy rights and patents?
If the Mod Group is violating someone Copy Right, then how can WB, or Bethesda, or Tolkien Estate know in good faith that there isn't more content within the mod violating other persons intelectual works.
How do they know that the mod wont harm the brand of LOTR?
What if WB had LOTR video games in the work, and this cannibalizes sales?
Why cant the mod group gain a legal licenses to use the LOTR IP?
Why do they deserve a special exception to use someone else story world without permission?
Why can't they make their original content for their mod?
I'd argue that before adressing any of those points the coorperations should adress why no works will ever be allowed to enter the public domain ever again.
All the rules for copyright and the enforcement thereof were kind of predicated on the idea that eventually any new creation would become the property of everyone. The tradeoff being that in the meantime the original creator could wholey controll their works, and the profits that are derived from them. This benefits everyone. There are many reason why this is an agreeable solution to everyone, but the main point is the concept that eventually works become public domain. This is adressing the permeability of creative works, especially fictional narratives and characters, within our shared culture.
That said, in answer to your questions:
(Copyrights and patents are two completely different things. I'll adress copyrights because I'm not overly familiar with patents)
Legally: whenever and whereever in any situation and with hyperbolic punishments that far outwiegh the severity of the crime because of projections based on imagined revenue losses.
Morally: When someone else is trying to profit off your work and it shouldn't allready be public domain
I don't know? This is a wierd question. Why would any of those entities care if this mod is violating any rights but their own? The mod could violate every copyright that exists and it wouldn't effect WB's decision in any way AFAIK?
They either assume that it will or don't care and are just agressively defending their licensing rights regardless. Though the idea that a fan-created work can harm a brand seems completely ludicrous to me, especially in this specific case when we're discussing a 70 year old franchise that's hugely entrenched in our pop-culture.
Again, this is one of those ludicrous claims that companies try to make. They often say the same thing of piracy even though it's been proven wrong time and again. This is another one of those hypothetical questions that doesn't really seem relevant. The real question is "Is there any way this fan-made no-budget mod can in any way effect the sales of an officially licensed game."
The mod group could probobly gain the license to use the LoTR IP. If they had millions of dollars and providing the WB license isn't exclusive. Then you also get into the question of which LoTR video game license do they want? The book adaption games and the movie adaption games are two seperate licenses (or at least they were last time I checked). Basically it's prohibitavely expensive for individuals to license multimillion dollar IP's. There might be some method where they can ask for approval for their work, which would exempt them from the licensing or provide an extremely limited license, but I'm not overly familiar with that and as far as I know it's entirely a goodwill thing for the companies that do it.
Because the story world from LoTR was first published in like 1934 or thereabouts and should be public domain. Why does the Tolkein estate deserve a special exemption from the laws of public domain?
People like to pay omage to things they are fans of? Why do so many people write fanfics, draw fan art, hum songs that they didn't personally make up? Why do the people at WB movie studios and the esteemed Mr Jackson not make up their own fantasy movie? Why did they need to use someone elses content?
A better question would be "Why is Peter Jackson the only movie director allowed to create LoTR movies?" Is it because he's rich? Is there something in his previous work (Bad Taste maybe?) that somehow qualifies him for the transition of the most influential fantasy novel of the last century to cinema? Is it because he's from New Zealand?