There is lots of ambiguity as far as how the Elf works in the
original incarnation of D&D from 1974. Elves were a blend between
fighter and magic-user (MU), although you had to choose a class to
play each adventure, and it was anyone's guess how saves, hit dice
and level advancement worked.

    Elves: Elves can begin as either Fighting-Men or Magic-Users and
    freely switch class whenever they choose, from adventure to
    adventure, but not during the course of a single game. Thus,
    they gain the benefits of both classes and may use both weaponry
    and spells. They may use magic armor and still act as
    Magic-Users.  However, they may not progress beyond 4th level
    Fighting-Man (Hero) nor 8th level Magic-User (Warlock). Elves
    are more able to note secret and hidden doors. They also gain
    the advantages noted in the CHAINMAIL rules when fighting
    certain fantastic creatures. Finally, Elves are able to speak
    the languages of Orcs, Hobgoblins, and Gnolls in addition to
    their own (Elvish) and the other usual tongues.
    - Men & Magic, p. 8

That's pretty much it, other than a paragraph about Elves in
Monsters & Treasure which you may want to pick and choose bits from
to apply to PC Elves:

    ELVES: ... Roll a four-sided die for level of fighting and a
    six-sided die for level of magical ability, treating any 1's
    rolled as 2's and 6's(magical level), as 5's... Elves have the
    ability of moving silently and are nearly invisible in their
    gray-green cloaks. Elves armed with magical weapons will add one
    pip to dice rolled to determine damage, i.e. when a hit is
    scored the possible number of damage points will be 2-7 per
    die. Elves on foot may split-move and fire...
    - Monsters & Treasure, p. 16

This lets you know that the Fighter and MU levels don't progress in
sync, at least as far as NPC Elves. Anyway there have been tons of
variations on Elves and how they work over the years, many being
based on splitting XP and averaging hit points as levels are
gained. I have settled on something simpler, so here in a nutshell
are my OD&D Elf house rules, including my take on the Chainmail
abilities mentioned above.

Elves: Elves start as a combined Fighter/M-U, both at 1st
level. They can allocate earned experience to either class, or to
both as desired. Hit points are calculated normally when a level is
gained in one class, rolling all hit dice for that class (e.g. roll
4d6 for a 4th level Fighter) and keeping the previous total if it is
higher (at first level, take the better of the two rolls). They have
the benefits of the stronger class for saves, weapons and armor use,
but can only cast spells in magical armor or Elven chain.

- Elves of 9 or higher INT can speak the languages of Orcs,
  Hobgoblins, and Gnolls
- Elves are immune to ghoul paralysis
- Elves impart +1 damage with magical weapons
- Elves on foot armed with bows may half-move and fire without
  penalty
- Elves spot 'something is amiss' on a 1-2/d6 when passing near a
  secret or concealed door, and detect secret doors 1-4/d6 when
  actively searching

So there is no dividing hit points by two, which is how Gary Gygax
famously said he handled Elves (a variation of that is what I used
in my first OD&D campaign [0]). I also don't allow anything like the
Moldvay B/X Elf, which tracks a single hit dice and XP total and
allows all weapons, armor and spells to be used together. I now find
the former is too fiddly, and the latter misses the feel of the
original rules, despite being a bit simpler. I also don't allow
infravision for Elves, the original rules don't mention this until
the Greyhawk supplement.

And what about the 'split-move and fire' ability? In my OD&D games,
stationary archers can fire twice per round, or half-move and fire
once. Elves can do a half-move and still fire twice.

This is all subjective of course, but after having an Elf character
in my Nolenor campaign [1] use these rules for a few dozen sessions
and ending at level 4/4, I felt these rules definitely played better
in practice than my prior approaches.

[0]: gopher://gopher.smolderingwizard.com:70/0/rpg/player_and_gm_resources/odd_house_rules.txt
[1]: gopher://gopher.smolderingwizard.com:70/1/rpg/play_reports/nolenor