Should my characters get hungry? Should they eat? Should they become aroused? Should they bark like a chicken, or crow like a pig?
Again and again, when writing the only should is: you should write — the story won’t write itself, and you should use proper and clear language — without it your story is unreadable, or not understandable.
Beyond that, it’s just a question of what matters. You will find novels where the characters never go to the bathroom, never eat, never sleep, never sneeze, etc. You’ll find others where they do often. Obviously it is assumed that these activities are being engaged in, at other times it is quite clear that the author did not consider it as you have no room within the scope of the narrated time-frame for such to have happened.
You will never please everyone. Some people what to see everything. These people read Wheel of Time. Some people want nothing of the sort — I’m not sure what they would read because, at the minimum, food is generally going to come into things somewhere.
Should your characters have sex? Well, maybe. If you’re writing for young children, this may be a very peculiar question, and one that should be approached with caution as most feel that such things are rather inappropriate; certainly one should assume that graphic and explicit sex ought to be avoided in this situation as far as the culture of most English speaking readers are concerned; the values and mores of other segments of humanity I cannot implicitly speak for.
Should your characters eat? Well, at the very least, they should eat within your own mind. This avoids them going three days without a single moment to have a bite of something and not being the slightest bit affected by it. Then again, maybe you’re writing a very simple fairy story, and people don’t tend to worry about such trivialities as eating in those, except at banquets or the like.
Should they sleep? Again, it’s probably best to assume they do, and then decide when and where it might fit to show this — or not.
Should … yes, and no. Tell your story. Some conversations will take place over a glass of wine. Some will happen while trying to decide where to eat or what. Perhaps it will be necessary for the large carnivore to burst into the toilet where the character is currently occupied by …
But do not tie yourself down to necessary. That’s a sticky word. It implies that the scene, detail, whatever is vital, inviolate, unremovable. No. Not necessarily. Sometimes little things that hold no import to the plot or the larger story are in there just to keep the setting real, to keep the people real. Does it matter if Lauren wears green shoes with her dress? No, not typically. It does, however, matter in the sense of it gives little clues about the person that Lauren is. Does it matter in the slightest if Salencia is wearing a pink shirt? Well, once, actually, but any other times — no. But then again, yes — if I do it often enough it becomes evident that her favourite colour is “dusty rose” (that’s true, by the way, she loves that shade of pink). It’s Bilbo Baggins and his pipe — it hobbitises the character, gives him depth and shape.
You should leave out tedious details. If you learn nothing about the character to describe, in detail, how they comb or brush their hair — don’t. If, however, they brush/comb their hair in some remarkable way — show it! In the former, it suffices to tell — “she combed her hair, washed her face, and headed to the party.” In the latter it does an injustice to leave out the scene of the complex, Wallace & Gromit style automatic hair combing device, though once it’s established it might be best to skip it in later uses, unless there is some literary device served by showing its repeated use; maybe it is quirkily changing over time, or in the case of W & G’s movie about the Were-Rabbit, we learn that Wallace is, in fact, losing weight.
A good rule of thumb, if you are bored and don’t give a damn about what you’re showing, just tell it. If telling it seems like tedium and padded word count, then don’t even bother to mention it. You can never go wrong by assuming that, if you don’t care, your reader won’t care. True, some readers will, but probably not the ones who want to read a story you’d care to write — best to write for yourself and entertain the people who read as you do. You may or may not get better or worse sales for it, but it’s safe bet you’ll enjoy the process of telling the story far better. And anyone who writes for the money is probably someone who believes they’ll get rich playing nickle slots in Vegas; true, it happens, but it’s always pure, outright, dumb, blind luck.