Aiks, it makes me very happy to read your first report on OFS.

Now you have read the essay a first time, here are a few pointers that i have worked out over the years.
1. The first section implicitly follows a conventional Oxford approach to definition, whereby one begins by looking at all the things that are called X, rejecting some as not really X, and thereby arrive at a theory or definition of what X is. In other words, there is more of a method at work here than one first suspects - and the method concerns words and their meanings or definitions - and yet the conclusion is that, while fairy stories can be defined as stories that touch on Fairy, 'Fairy' itself cannot be defined.
2. Observe how, after stating that 'Fairy' cannot be defined, Tolkien offers the suggestion that it may be 'translated' as 'Magic', but then, much later, in the section 'Fantasy' he retracts this translation, offers instead 'Enchantment' and declares that Magic is what evil magicians do. This strange 're-translation' is i think at the heart of things, and has a clear parallel in the LOTR when Sam says he wants to see 'real elvish magic' and Galadriel explains the difference between her art and the deceits of the Enemy.
3. But think on this: Lorien endures in History because Galadriel wields one of the Three, which though untouched by Sauron are - by way of the story of Celebrimbor and his 'friend' who taught him much lore - as near as elvish art can get to Magic. Ultimately, I suggest, OFS shows us that Sam's expression was correct - Lothlorien is at its roots 'elvish magic' and when Frodo offers Galadriel the Ring, Galadriel herself must acknowledge this. But this is a big reading perhaps better drawn out in full elsewhere.
4. The section 'Origins' is the (usually overlooked) key to the essay and to Tolkien's 'philosophy' in general. Tolkien says that when we engage in 'fantasy' by joining words to make new ideas we already have an enchanter's power, on one plane. Scholarly readers of the essay prefer to ignore this, but it seems to me that Tolkien is saying that language is magical and that, as speakers of language, we mortals have ourselves 'magic' power. In a nutshell, magic is found among us in our use (and abuse) of language - or to spell it out in full in light of the double translation of 'Fairy': with our magic we may discover the Divine face within us by sub-creative fantasy = telling fairy stories; or with our magic we may dominate, oppress, delude, cheat, and spin webs of fake news and propaganda.
5. The section 'Children' is concerned with a few things. Firstly, Tolkien is struggling against a late 19th-century academic reading of History in which humanity has advanced from 'primitive' or 'savage' to enlightened western mind. Such presuppositions prompted the late Victorians to read fairy stories as the stories from 'the childhood of mankind'. Tolkien thinks this is nonsense: he thinks that people always tell fairy stories, though our stories today are certainly different from those of our distant ancestors. But at the same time in this section, Tolkien is grappling with the introduction of the Necromancer into the center of the sequel to The Hobbit, which he recognizes means that he is writing a fairy story that is not quite suitable for children.
6. There is a modern scholarly edition of the essay (edited by Flieger and Anderson) that presents not only the 1947 essay but also the earlier drafts, allowing us to see the change from the 1939 lecture in Scotland to the essay penned in summer 1943. What comparison reveals is that the whole section 'Fantasy' is new. This section is generally considered to hold the theoretical core of the essay, which suggests that these ideas were clarified in Tolkien's mind as he penned the story from Moria to Isengard. As with Sam and Galadriel, so more generally the essay and the story are intimately bound together.
7. Having reached the end of the section 'Fantasy' most readers are exhausted but it is actually in the last discussion of the use of fairy stories that the essay opens up and provides a key to the story of LOTR. For example: the account of Theoden's bewitchment by the words of Wormtongue, of Gandalf's calling on the king to take courage so he can offer counsel, of the king's subsequent encounters with hobbits and ents - the stuff of the fairy stories of Rohan, which spur his recovery such that Theoden can see through the enchantment of the voice of Saruman. Here we have the blending of the old northern theory of courage with Tolkien's idea of magic and enchantment, such that the value of fairy stories is properly placed in the correct order of recovery from necromancy: courage - counsel - fairy story: recovery. This in my opinion is the deepest theme of LOTR, and may be found not just in Rohan but throughout the story, at least as it concerns mortals.