AceCalhoon's answer to this question got me thinking, is there any reason to believe that the D&D source books assume a specific system of ethics, such as deontology, virtue ethics, or consequentialism? Are these terms or ideas ever mentioned in a Player's Handbook or Dungeon Master's Guide? Do the D&D source books ever attempt to ground their alignment systems in a particular ethical system, or is it purely a mechanical distinction?
No, they don't. The origin of the ethical system encoded in the alignment system is teleological: different moral approaches to reality exist because cosmic forces created them, and your alignment is literally which cosmic forces you are aligned (aka “allied”) with and working to further in the Cosmic War (whether you know it or not).
The Cosmic War is not a setting assumption that survived beyond 1st edition AD&D. Every edition after just held on to the idea alignments (which no longer indicate alignment with anything), with various tweaks to the specific list, because of tradition. No attempt to ground them in a real or reasonable ethical system has ever been attempted; only post hoc justifications and analogies have been attempted, and then only for the pragmatic goal of explaining them to a reader who has very likely never read Three Hearts and Three Lions or anything by Michael Moorcock regarding Cosmic Law and Chaos.
No. The alignment system is largely a hold-over from early D&D that was evolved into it's own new beast, separate from it's original inspirations. Oddly, the D&D alignment system is well-known even outside of RPG circles as a simple method of describing ethical caractitures.
In OD&D it was theoretically tied to the forces of Law/Good, Evil/Chaos, and Balance, which warred constantly in what was called the 'Cosmic War', though many people, myself included, have never played the game that way or had a campaign world with that kind of set up.
In game (in 1st through 3rd edition D&D, and I will also 5e if I ever play it again and use the actual alignment system), I always tell my players (or ask my GM) what ethical system we will be using for the campaign. I have played with multiple different implementations of all the ethical starting points you mention, as well as other, and they all work quite well. Utilitarianism tends to make for a bleak, awful existence as man's alignment and ultimate fate is a matter of luck (and skill, but that just makes it worse). Deontology works well, and can generally just fade into the background if you don't want to focus on alignment too much. Virtue ethics is awesome and totally captures the medieval genre and feel. Psychological Egoism is hilarious.
The point I'm trying to make here is that once upon a time it was initially kinda grounded in a particular fantastical ethical system, but then it stopped being that way. Furthermore, the way it evolved was a good thing and allows you to tie it easily to any ethical system you'd like in your particular game world. Some particularly strange and poorly thought out systems-- like moral relativism-- don't work very well, but the systems you listed and many others are fully compatible with all editions of D&D (not including 4e).
4e decided Law=Good and Chaos=Bad, and thus is a little different. This sort-of re-grounds it in the original inspirations for the system, but because people are no longer familiar with the particular tropes necessary to engage with the game in that alignment system it usually just ends up either ignored or Hobbesian. Certainly the Law=Ultimate Good thing supports a Hobbesian approach.
No, that's up to the players involved in the campaign. The alignment system in D&D is not meant to be a psychological profiling tool. Its simply meant to give some ability for players and DMs to generate scenarios where morality of an action can come into question. There may be no question that Lancelot the Paladin is a Lawful good Scout in good standing. What happens to him when he is forced to kill a hostage in order to avoid epic destruction and loss of life? The "Answer" is irrelevant because the answer I give in my campaign, is different than in yours. Certainly Michael Moorcock's books are a source of inspiration for the original concept (and if memory serves was mentioned in the DMG). I believe that alignment was added to the game not to inject a "cosmic war" concept but to provide a framework for players to have an action boundary to allow for dramatic actions to occur. It should be pretty obvious (even if the debates on an action define it during the game ) where each of the alignments stand to the players. I've likely spent no more than 2mins explaining the idea to new players. One thing that has been removed from the game (but I firmly believe in) is the XP penalty for out of alignment actions. This is not a punishment penalty in my view but a way to reflect that out of alignment actions would have real consequences. Thus when Lancelot puts a sword thru Princess Penny's tearful blue eye to stop Dastardly Dan from destroying the kingdom, it's an actual sacrifice that made Lancelot spend quality time thinking about his commitment to lawful good (and therefore drop a little XP).