Short answers, pulled from the story.
The word orc comes from the Old English term orc, which appears in the poem Beowulf as part of the compound orcneas, meaning roughly "demon-corpses" or "corpses from the underworld". The Anglo-Saxon word is generally thought to derive from the Latin orcus, meaning the underworld or Pluto, though Tolkien himself expressed doubt about that connection. Tolkien chose the word for his own monsters purely for what he called "phonetic suitability" reasons.
Tolkien created orcs to supply Middle-earth with a continuous supply of enemies that heroes could kill without moral compunction, describing them in The Monsters and the Critics as "the infantry of the old war" ready to be slaughtered. The scholar Tom Shippey argues this narrative convenience drove their invention. Tolkien also acknowledged in a 1954 letter that orcs were "fundamentally a race of 'rational incarnate' creatures, though horribly corrupted".
Tolkien offered multiple inconsistent explanations for orc origins across his writing. Possibilities include: creations of Morgoth bred from slime by sorcery in The Fall of Gondolin; enslaved and tortured East Elves in The Silmarillion; Avari elves who turned evil in the wild; fallen Maiar spirits; corrupted Men; or beings produced by Elves mating with beasts. In a letter dated the 21st of October 1963, Tolkien confirmed there must have been orc-women, suggesting orcs also reproduced sexually.
Yes, several critics have made this argument. In a private letter, Tolkien described orcs as "degraded and repulsive versions of the (to Europeans) least lovely Mongol-types". The journalist Andrew O'Hehir, writing for Salon.com, called them "a subhuman race that is morally irredeemable and deserves only death", while the literary critic Jenny Turner, writing in the London Review of Books, called them "a northern European's paranoid caricature". Both critics also acknowledged that Tolkien did not appear to have been consciously racist and that his work reflects the anxieties of his era.
The 1974 original edition of Dungeons and Dragons gave orcs a pig-faced appearance that Tolkien never described in his writing. Later editions shifted orcs from bald to hairy, and the third version made them gray-skinned, departing from the more complex colour descriptions in the first edition Monster Manual of 1977. The pig-headed design became the dominant visual image of the orc in gaming.
Tolkien's writing suggests an unresolved tension on this question. The orc Gorbag in The Two Towers disapproves of what he believes is a comrade being abandoned, displaying a recognisable moral sense. Tolkien wrote in a 1954 letter that orcs were "horribly corrupted" but fundamentally rational creatures. The scholar Robert Tally noted that Tolkien repeatedly "humanized" his orcs despite portraying them as wholly evil, giving them a morality he never reconciled with their narrative function as guilt-free enemies.