The cherry scene actually does serve a purpose. At least at the end it does. At the very end, the flyer is trying to feed Littlefoot the cherry. But Littlefoot refuses to take it.
The purpose of this scene is twofold. First, it shows that not all dinosaurs have prejudice. This flyer willingly came up to Littlefoot, saw that he was hungry, and wilingly gave up his own food to help him. Considering that food is very scarce, the fact that this baby fllyer was willing to give up its meal, the meal which might be the only one he'd get in a very long time, to a total stranger, who is of a different species, shows that some dinosaurs (though technically ptoersaurs aren't dinosaurs) not only lack prejudice against other species, but that there are kind dinos who will commit selfless acts for the sake of others, even those they never met.
The other purpose the scene serves is to show just how broken Littlefoot is. He just lost his mother and though he's hungry, he can't bring himself to eat it. He's so distraught that he just doesn't care about living. Littlefoot, at this point, is kinda suicidal. Not in the sense that he's actively trying to kill himself, but in that he is not doing much to help himself. It isn't until Ducky shows up and he realizes she's in the same boat as him (or a similar one at least) that he snaps out of his depression.
As for the "my tummy hurts", this actually makes sense for Littlefoot to say. Loss can feel very gut wrenching, and Littlefoot has never experienced this before. He isn't saying it out of hunger; he's saying it out of depression. It's not an immature thing to say. And keep in mind, Littlefoot is a young kid; he's not really that mature in the movie and has shown some less than pleasurable moments. One example is when he tries to force Petrie to fly and keeps running despite Petrie desperatley telling him to stop. Now this wasn't a mature thing for him to do and pretty cold. However, I do like that it's in the movie because it shows that no, Littlefoot is not always mature because he's a kid and he still has so much to learn.
But while I do think that Littlefoot has some immature moments, the "my tummy hurts" certainly isn't one of them, given the sitiuation. He just lost his mother and that horrid feeling of loss, anxiety, and guilt is going to make his stomach hurt. That's how these powerful emotions can work. It's nothing I find remotely funny or something to smirk about.