What impact adaptations have on their source material?
Depends on how well known the book was to begin with. What immediately comes in mind to my head in terms of effect are three works: Forrest Gump, Shawshank Redemption, and Water Margin.
Most people probably don't know that Forrest Gump started out as a book. Nor the fact that it also has a sequel. Nor that certain events in the book happened that did not occur in the movie (e.g: going to space). Nor that Forrest Gump has a contrastingly different character. I can't even name the author, sooo yeah. Impact is there but it has not propelled a lot of people to read the source material otherwise aforementioned statements would be more well known. Quality of movie and its ending also satisfied me to such an extent that I don't really want to read the book. Knowing of its differences.... even less.
Shawshank Redemption became its own celestial entity in media because of how well the movie was portrayed. It's a more known fact that Stephen King wrote the source material. But not many people outside the literary realm knew this because the film's title did not hook people to watching it initially. Why watch something called a "Shawshank Redemption" if one never even heard of it as a book. Even after the movie became popular, I know most people haven't read the book because I have not seen many viewpoints on the significance of Red's change in physical appearance from the book to the movie. In fact, I would argue (without reading the book) that the movie change actually enhances some of the themes of the work. The movie is so good and has such a resolved ending that I also have no desire in reading the source material.
Water Margin is much more widely known in the Eastern Hemisphere, having a historic influence in both Chinese and Japanese culture. It has an entire list of adaptations ranging from TV to video games (Any video game nerd has heard of the Suikoden video game series, which is a loose adaptation of Water Margin). It is also one of the few works I know of that has essentially an erotic fanfiction adaptation of one of the book's story arcs become a literary masterpiece (Jin Ping Mei). It's like an old Marvel cinematic universe-style of origin stories leading to an Avengers-like army (of 108 people) of criminals. If you combine Robin Hood with A Song of Ice and Fire, you get something that resembles Water Margin. Water Margin's lack of inclusion from top books in world literature show how myopic, uniliterate, biased, and unilingual a lot of those list compilers are. That's another story though. Anyhow, its tv adaptations are well known in China and Japan. I believe one of those adaptations aired on the BBC with an English dub for a time. Here's the thing though: because of the book's legacy, most of the close adaptations were judged on how accurate they were to the book. Sort of like the initial reception towards HP Philosopher's Stone. The looser adaptations became their own thing (Jin Ping Mei, Suikoden) and did not have much direct impact to the source material.
There's also the additional wrinkles with Water Margin the book. For one, it's written in Literary Chinese, which honestly is a language by itself outside of modern Chinese. The lingual departure isn't even something like Shakespearean English to Victorian English. It's more like Old English to Victorian English. But because the tales have been around for more than 900 years and are really well known, fans don't even need to read the work (translated or not) to still criticize certain TV adaptations for changing parts of the tale. So there has been no negative impact from adaptations because the book is essentially holy... and most people cannot/haven't even read it in its original source.
So in general, the bigger and well-known the source material is, the less potential for negative impact from adaptations. The level of positive impact depends on the quality of the adaptation. Bad adaptations are more likely to be ignored or seen as non-canonical if the source material was already well known (Song of Ice and Fire for both extreme ends of the spectrum). However, if the source material is not well-known, the adaptation most likely brings short-term material gain but positive impact is dependent on how good the adaptation was. If the adaptation is too good (Forrest Gump or even something like Dragon Ball), particularly if its a movie, then the source material gets only a marginal increase as the adaptation probably satisfied its audience enough. Either the adaptation has to be in the slightly bad to merely good range, leaving the audience wanting more, or creating a sort of cliffhanger for a sequel, would there be a large positive impact to the little-known work. This is evident in a lot of 1-2 season anime nowadays, where they intentionally keep the story unfinished to hook people into reading the source manga/visual novel/literature. I would argue that if LOTR was a little-known work, the first two movies' kinda cliffhanger would have created that impact.
I wanted to answer all the questions in the opening post but uhh I've typed too much already. Maybe save it for next time.
The visualisation of all realms made it for me a world to touch in a sort of real time, and yet standing fully alone and independent from the real life I have as well. My characters have through all available a 'real life' touch and I am thankful for those who made those creations. 
I would not agree that it's impossible for adaptations to be faithful on a deep level, but for ROP, there's very little they can be faithful to, especially without the rights to posthumously published materials (it remains to be seen if they're granted many case-by-case exceptions by the Estate, beyond the map of Númenor, which they've already used in marketing material). Then again, Amazon's decision to condense all the major events of the Second Age into less than a single Númenórean lifespan—as opposed to exploring one portion of it in detail, or even condensing it into two chunks (one focused on the forging of the Rings, the other on the Downfall of Númenor and the Last Alliance) with a timeskip between them—means they'll be diverging significantly from what little is available to them. But at this point in my life, I can only devote so much energy to complaining about this.
