D&D halflings were 100% hobbits, half elves and half orcs (I can't think of any pre 70s source except LOTR that has half-elves and half-orcs), ditto, but elves always existed in a weird sort of "maybe Tolkien elves but maybe not" because of how short they were. Gnomes are about the only non-Tolkien race for sure. (For Tolkien, gnomes was a term for Noldor - who were basically grey elves).
Well, EGG didn't like people pointing out that his races all came from JRRT, so he sort of post hoc tried to fudge up elves a bit. Gnomes are not a demi-human race pre-1e either, so a late addition in that way, as are half-elves I believe. Half-orcs may exist in some source pre-1e, but only become playable there as well. So the 'core' races seem to all start out as Tolkienesque for sure, and then Gary starts messing a bit with elves, adds gnomes, and obviously has to change hobbit to 'halfling'. I never understood why he was so annoyed by the whole races thing though. Gary was a quirky guy though...
Look at it this way, Tolkien wasn't starting from nothing, his expertise was in old English folklore. Dwarves, elves, and various forms of 'small people' certainly fit within the overall genre, and JRRT got them from SOMEWHERE, including Celtic myths which are part of the substrate of English folklore. However, I would expect an entirely non-Tolkien inspired D&D (which Gary tried to claim at some points) to have Dwarves and some sort of 'Alf', but probably less humanlike and more just non-playable monsters. Maybe the answer is really these all came from Dave to some degree, I dunno.
Gygax did not independently come up with the idea of armies of Elves and Dwarves who might fight alongside human armies. The whole notion of turning fairy stories - with their Elves and Dwarves and the like - into more-or-less naturalistic fiction, where the faerie people have homes that might be visited and lived in, and inhabitants who might be interacted with, in an "ordinary" way, comes from JRRT.
Right. This is the key point: the notion of "demi-humans" who are economically, socially, politically, and culturally variants on humans, so that they can adventure with humans, have kingdoms and armies that operate on the same map and in the same way as the human ones, etc - this is all derived straight from JRRT. Chainmail doesn't even bother filing off the serial numbers!
Bit of a "yes but" here: Pratchett was British, and Howard (and Lieber and Lovecraft) were pretty much unknown in Britain in the 40s and 50s. They certainly were not part of pop culture. We know Pratchett was playing early D&D around 1975/76, and that is probably what brought him into contact with those authors.
Quite ironic since Moorcock was one of the authors to popularise the word "sword and sorcery"
Moorcock was editor of a British Science Fiction magazine in the 60s, and was personally responsible for introducing the likes of REH to the British market. As a Londoner he had more access to Americana, and cites Edgar Rice Burroughs as an early influence. Thanks to the Tarzan movies ERB was known in the UK.
The spell system did "sort of" that does not mean the Vances stories had wish spells ,magic jar, lightning and fire balls or Leomunds tiny hut. Nor that any casters in Cudgels story ever had the ability to cast the number of spells a D&D caster did. Re-minding ones self of a spell did not require a nights sleep in Vances fiction that I recall either. The original D&D core spells like lightning bolts and fireballs were made in Chainmail and had no memorization limits to speak of ... it was tacked on later.
