This root for friendship and devotion first appeared as ᴹ√NIL or strengthened ᴹ√NDIL “friend” in The Etymologies of the 1930s with a number of Quenya derivatives of similar meaning, the most significant being the suffixes ᴹQ. -nil or -dil, which Tolkien said was the equivalent of Old English “-wine” (“-friend”). In The Etymologies, ᴹ√DIL was an unrelated root meaning “stop up, fill up hole” (Ety/DIL). The strengthened root ᴹ√NDIL was mentioned again with the gloss “love, devotion” in The Notion Club Papers of the 1940s (SD/241, 305).
The unstrengthened form √NIL appeared in a letter to David Masson from 1955, where Tolkien said “√NIL means to love as a friend or equal”, as opposed to √(N)DUR which meant “to show special interest in things such as trees, astronomy, gems, medicine, sea, etc.” (PE17/152). Tolkien went on to say that, properly speaking, -(n)dil could apply only to persons and -(n)dur should be used of things, with names like Meneldil and Anardil being “Mannish” misuses of the suffix.
The root appeared again as √(N)DIL “to love, be devoted to” in the draft of a letter to Mr. Rang from 1967, where Tolkien clarified that it described “the attitude of one to a person, thing, course or occupation to which one is devoted for its own sake” (Let/386). This seems to be the only place where Tolkien clearly indicates the unstrengthened form is √DIL. Tolkien again clarified the distinction with √(N)DUR in a footnote:
> This provides the key to a large number of other Elvish Q. names, such as Elendil “Elf-friend” (eled+ndil), Valandil, Mardil the Good Steward (devoted to the House, sc. of the Kings) Meneldil “astronomer” etc. Of similar significance in names is -(n)dur, though properly this means “to serve”, as one serves a legitimate master: cf. Q. arandil “king’s friend, royalist”, beside arandur “king’s servant, minister”. But these often coincide: e.g. Sam’s relation to Frodo can be viewed either as in status -ndur, in spirit -ndil. Compare among the variant names: Eärendur “(professional) mariner” (Let/386).
Neo-Eldarin: For purposes of Neo-Eldarin I would leave the unstrengthened form of this root as √NIL to retain the use of ᴹ√DIL “stop up, fill up hole” from the 1930s. I would also assume that √N(D)IL mainly refers to “devotion”, as opposed to √(N)DUR which mainly refers to “service”. Hence Elendil = “Elf friend” but Valandur = “Servant of the Vala”.
A root appearing in Notes on Names (NN) from 1957 with the gloss “child” (PE17/157), and again in the Quendi and Eldar essay of 1959-60 with the same gloss (WJ/403). It was the basis for the words Q. hína and S. hên “child”, which were probably inspired by the Adûnaic patronymic suffix -hin that Tolkien introduced in the 1940s as part of Êruhin “Child of God” (SD/358), originally an Adûnaic word but later on used in Sindarin (Let/345; MR/330). This root might be a later iteration of the early root ᴱ√HILI from the Qenya Lexicon of the 1910s whose derivatives had to do with children (QL/40). As evidence of this, the Adûnaic word was first given as Eruhil (SD/341).