Hi John, and welcome back!
Firstly, a couple of clarifications...
(Players Guide p10)
* Fighters have multiple attacks per round versus opponents with
fewer than 3 HD.
* They have this advantage from 2nd level and up (as they have just the 1 HD at 1st level).
To answer your second question first:
The DD rule is a "simplification" of the rather complicated mechanic that is touched on briefly in the 3LBBs, explained further in the FAQ article appearing in The Strategic Review, but ultimately derived from Chainmail's normal (as opposed to fantastic) combat system.
As far as the 3LBBs are concerned, the first clue is in the fighting capability stats of the player types, noted as Man/Hero/Superhero equivalents. The "Man" part of the fighting capability is a figure's "normal" fighting equivalence back in Chainmail. This is then "translated" into a more general rule for all monsters in Monsters & Treasure (p5), which explains that monsters fight as one "man" per HD, so a Troll rolls 6 attacks per round versus "normals" because it has six HD.
The FAQ article goes on to explain further:
"A super hero, for example, would attack eight times only if he were fighting normal men (or creatures basically that strength, i.e., kobolds, goblins, gnomes, dwarves, and so on)."So, there is one attack per HD/level versus "normal men".
"Note that he is allowed one attack for each of his combat levels as the ratio of one Orc vs. the Hero is 1:4, so this is treated as normal (non-fantastic) melee, as is any combat where the score of one side is a base 1 hit die or less."This is a bit more complicated, but it says:
A. When the defender has base 1 HD (or fewer) combat is treated as "normal".
B. When the ratio of attacker's:defender's HD is 4:1 combat is treated as "normal".
C. When combat is "normal" the attacker is allowed one attack roll for each of his HD.
What is not given explicitly is an absolute definition of what creatures are "normal".
Instead we have various "clues" as to what is considered normal including: Dave Arneson's "flunky" types in Blackmoor (including regular men-at-arms) were equivalent to 2 HD (had 7 hp), the definition of "Men" extends to 2 HD Cavemen, 2 HD gnolls are still considered rank-and-file troops in S&S, and also the definition of when fighters, clerics and magic-users are deemed to be "heroic" as opposed to "normal".
There is certainly contention as to "how many HD" do normals have, because ultimately it's a Chainmail concept where HD don't apply, so it's not an exact science. EGG later (AD&D) tightened the definition of normal further, but OD&D remains a woolly mix of Arneson and Gygax inputs.
Delving Deeper boils all this down to the one simple statement: "one attack roll for each of his own hit dice versus enemies with fewer than 3 hit dice".
IMHO this covers Arneson's flunkies as well as the two ways combat can potentially qualify as "normal" per the FAQ (the "base 1 HD" kind, and the "4:1 HD" kind), and also lines up pretty neatly with the definition of "Men" and "man-types" in the 3LBBs, as well as the fighter's transition from "normal" to "heroic" type in the fighting capability chart.
Regarding the 4:1 ratio business from the FAQ, you'll note that even the 12th level DD fighter has 11 HD, so multiple attacks are never applicable to 3 HD types anyway.
And to (finally!) answer your first question:
There's nothing in the 3LBBs or the FAQ that says clerics and magic-users shouldn't also have multiple attacks per round. Neither is there anything to say that they should. Folks have discussed this very thing on these boards, and I suspect some give multiple attacks to everyone, which is perfectly okay.
For me personally, I believe that combat is the realm of the fighting man, and to dish out combat advantages to the other classes diminishes his worth somewhat. Granting multiple attacks to clerics and magic-users is a bit like granting spell casting to fighters. It's up to the individual referee to decide if they want to blur the classic "division of capabilities" in that way.
Clerics, magic-users, and fighters are treated equally, however, in that each of them are no longer subject to multiple attacks per round when they have attained 3 HD.
Hope this helps some