I think the complexity comes because how you use the term can be varied and I believe there is opportunity to use "orange" as both a count and non-count word - at least informally.
My son was hungry so I gave him some orange as a snack.
Here, you've given him an unknown amount of orange. The implication is that you've left out "of my" or "of an". This is informal but will be understood and I've said it myself as a native speaker.
Similarly, a messy eater might need to be cleaned up:
I need to wipe you off, you have some orange on your face.
Here, the elided word is "juice" or "pulp" but the sentence is sensible in informal English.
In the US, at least, it's common to give children wedges of orange that are unpeeled - so they can shove the whole thing in their mouth and make silly faces. In such a case, you could certainly say:
He was eating some orange wedges.
You ask whether you can be specific about segments - you can. If it's important that the amount is clear, you may be as specific as you like.
- He happily ate half of an orange but didn't want the rest.
- She would only eat three orange segments for snack today.
- She ate some of her orange but gave the rest to her brother.
And this isn't only for oranges, by the way.
- I gave my son some banana in his lunch today.
- There's some carrot in the salad, is that OK?
English is a pretty flexible language and, to be honest, we get a bit lazy about being specific about what "some" is describing. In the sentences above I could have more correctly said:
- I gave my son some slices of banana in his lunch today.
- There's some shredded carrot in the salad, is that OK?
But... if the preparation of the food doesn't really matter or you're talking to someone who can see the preparation, it's acceptable to (informally) omit the words. So, use it with caution but know that it's not perfectly impossible to use the construction you're trying to use!