Seems legit. Real people having a hard time finding meals can eat like that, and hard-luck adventurers are the kind of people who might see a lot of time between meals.
For someone who can afford to eat though, going hungry is foolish. Having a full belly when you have the opportunity to get one is just a matter of being prepared for the worst when you're venturing into the unknown. You never know when your mule with all the food is going to get eaten by a dragon or your pack might get dropped down a chasm, and then your carefully-timed starvation diet becomes actual starvation, with who knows how long before your next meal.
Mechanically, it would not be unreasonable for the DM to rule that being hungry can cause Disadvantage under the right (or wrong, I suppose) circumstances. If you haven't eaten for three days and you're sneaking through the orcs' kitchen, even revolting cooking smells are potentially distracting and might make the difference between failure and what would have been success—which is nicely modelled by Disadvantage. Similarly, exhausting activity such as climbing or swimming might be harder when your body is being systematically denied fuel.
So yes, you only need to eat every four days to avoid starvation. But as we well know from real-life experience living, going hungry sucks and is worth avoiding if you can, especially if you have any doubt about where your next meal is coming from.
The helmsman could be weird...
Neither constructs, elementals, oozes, non-native outsiders, plants, nor undead need to sleep, therefore the helmsman could be a creature with any of these types or take feats or prestige classes that transform him into any of these types. However, a helmsman could also take...
- The general feat Tomb-tainted Vitality (Libris Mortis 31), among other effects, grants the creature the ability to go without food and sleep (yet the creature must still hydrate—whatever). The feat's prerequisites include the feat Tomb-tainted Soul (LM 31) and a nongood alignment. The feat gives the creature a "freakish skeletal appearance"—which seems a little judgy. Also, giving the helmsman these feats likely makes naming the helmsman Charon no longer optional.
...Or the vessel could be trapped (but in a good way)
Using the feat Craft Wondrous Item (PH 92) the vessel could have installed near the wheel a magical trap (DMG 74) that's a boon trap (Dungeonscape 135). Boon traps are horrible, notoriously both vague and broken, but this boon trap will be used only for...
- The 4th-level Clr spell remove fatigue [trans] (Book of Exalted Deeds 105) grants 1 touched creature/2 levels the benefits of 8 hours of restful sleep (but casters, if they need rest, must still get it). The spell removes the condition fatigued if present and permits the target to rest 1 hour to remove the condition fatigued if, before the spell, the target had the condition exhausted.
The DM must decide on the boon trap's precise effects, but it probably won't cost more than 50,000 gp, which, while expensive for such a trivial effect, really is a trivial effect. Taking the wheel'll trigger the boon trap which will cast the spell remove fatigue on the creature, letting almost any creature serve as overnight helmsman.
Trivia
There're no penalties for not sleeping unless sleep's necessary for something else, like preparing spells afterward. However, everyone knows sleep's a thing, so folks sleep even if the game doesn't mandate they must.
For those who will not be constrained by petty, demanding reality, Elder Evils, under the additional sign of the apocalypse Appaling Fecundity, presents some rules for sleep deprivation, saying that
A living creature can go without sleep for a number of days equal to its Constitution modifier (minimum one). Thereafter it is fatigued, remaining in this state for a number of days equal to its Constitution modifier (again, minimum one); if it would become fatigued during that time, it is exhausted instead. Each day after that period, the creature takes 1 point of Wisdom damage. If the total Wisdom damage exceeds its Hit Dice, the creature is affected as if by an insanity spell. (ElE 9)
The book then goes on to mention that during the Appalling Fecundity sign, one can't recover the Wisdom damage caused by lack of sleep (which is pretty clearly not the case for normal sleep loss). To clarify, the Wisdom damage accumulates until the creature falls unconscious, and lack-of-sleep effects (fatigue, exhaustion, Wisdom damage, insanity) are fixed only by sleep.
Although presented in the context of a Sign of the Apocalypse, these are decent (if long-winded) rules, finally published near the end of the game's run, for those who insist their characters needn't sleep. (Although anyone who insists his character needn't sleep will probably also insist these rules be ignored unless that sign of the apocalypse is present.)
Best Answer
Most of your constraints are solved with the updated Mystic class
With the March 3rd Unearthed Arcana Mystic class, you can, among other features, focus on one psionic discipline to gain a passive benefit. The Adaptive Body discipline says the following:
This doesn't solve the problem of not needing to drink, but you can get this benefit as a first level Mystic, meaning you can get most of want you want very early. Additionally, unlike most of the other options below, the requirement for sleeping is removed entirely, instead of just worked around with something like trancing. Ultimately, a Monk 15/Mystic 1 gains Timeless Body (described in detail below), which will remove all requirements for eating, drinking, breathing, and sleeping. Additional options are provided below:
The new Sorcerous Origins are an option
The Sea Sorcery Origin in the Feburuary 6th Unearthed Arcana has the Water Soul feature at 18th level:
Combine this with a wish (described more below), and problem solved. Though you will likely spend more time without this power than with it, and you don't grow into this condition steadily, like some other options.
If you wish to avoid playtest material, the following options are available with just the core rulebooks.
Petrification Solves all your problems:
Turning yourself to stone, or other such material, means that you don't need to sleep, eat, drink, or breathe. Though, it's basically like being dead. This can be useful if you have a very reliable way to remove the petrification and you need to entomb yourself for an extended time span. Like magical cryo-sleep.
Move to the Astral Plane:
The Astral plane is described on Pg. 46-7 of the DMG.
Since this plane is described in spiritual terms, a sea of thought rather than matter, it could be assumed that the need to sleep or breathe is also removed while you inhabit the plane. Though this is up to your DM, since the DMG says nothing about those two processes. Also, in previous editions, if you return from the astral plane to any non-timeless plane, the effects of time will accumulate retroactively upon entering the new plane. For example, returning to the Prime Material plane after ten Prime Material years in the Astral plane will cause you to age 10 years, and the hunger, thirst, and sleeplessness of 10 years all take effect instantaneously. Basically, you will die if you leave the Astral plane without taking some serious precautions. This is omitted from the 5e description however. Finally, you will likely have to actually shift yourself into the Astral Plane. Projection, as with the Astral Projection spell, will leave your body limp and helpless on whatever plane you originated from.
True Polymorph yourself into an intelligent undead or construct
True polymorph allows you to change yourself into another creature. There is no rule that you can't change yourself into an undead, which will give you undead nature. You could also change yourself into a construct. However, all your stats, including your mental stats, are replaced by the stats of whatever you choose, and its CR must be less than or equal to your level. Also, literally change into whatever undead/construct you decide. You will be subject to all of the limitations of that form. That is: don't turn yourself into something that cant speak or doesnt have arms to cast spells
Assuming the new form is suitable, you can polymorph yourself and concentrate for the full duration to make the change permanent.
Timeless Body solves hunger and thirst
A 15th level monk gains the timeless body feature. You no longer feel the crippling effects of old age, and no longer need to eat or drink as ki sustains you. You will still die of old age though, and you still need to breathe and sleep.
Elven Trancing is not sleep:
Elves can get the benefits of 8 hours of sleep by Trancing for 4 hours. The trance is just deep meditation; the Elf never loses consciousness. And so, elves technically do not need to sleep.
Wish that you no longer need to respirate to live
Assuming you can get your hands on a Wish you could wish that you no longer need to respirate. You will need to word this very carefully as to avoid any potential twisting of the words. And ultimately, the DM still has the authority to turn the wish down. You will also suffer the stress of a wish from not replicating a spell of the 8th level or lower.
Combining these gets you what you want
So, if you are an Elven monk and you find a way to cast a Wish spell (example, find a Luck Blade), you will be technically sleepless, and have no requirement for food, water, or respiration. All without being undead or a construct.
Additionally, gaining these benefits in this manner will keep them active at all times, not only while you are conscious.
Immortality Too?
If you make it to 20th level, you could potentially get the Boon of Immortality (DMG pg.232).
If combined with the options described above, you will also stop aging all together, become immune to all aging effects, and you will no longer die from old age. At which point, you will be effectively timeless, sleepless, and have no need to eat, drink, or breathe.