De schil van een sinaasappel ruikt fris, maar ik eet die niet op.

Because schil is a de-word in Dutch. Dutch nouns have grammatical gender, and schil takes the common-gender article de.

• de schil = the peel / rind / skin

This is something you usually just have to learn with the noun. If you made it a diminutive, it would become het schilletje, because all diminutives take het.

Yes, you could also say de sinaasappelschil.

Dutch often expresses this kind of idea in two ways:

• de schil van een sinaasappel = the peel of an orange
• de sinaasappelschil = the orange peel

Both are correct. The van structure is very transparent for learners, and the compound noun is also very common in Dutch. Dutch likes compound nouns, so you will often see both patterns.

Because een means an / one, so it refers to an unspecified orange.

• de schil van een sinaasappel = the peel of an orange
• de schil van de sinaasappel = the peel of the orange

So the sentence is not talking about one specific orange already known to both speaker and listener. It is either generic or based on an unspecified orange.

Because ruiken can work like a linking verb here, similar to smell in English.

• De schil ruikt fris. = The peel smells fresh.

In this use, the adjective describes the smell directly.

You use naar when you name what something smells like:

• De schil ruikt naar sinaasappel. = The peel smells like orange.
• Het ruikt naar parfum. = It smells like perfume.

So:

• ruikt fris = smells fresh
• ruikt naar ... = smells like ...

Because fris is a predicative adjective here: it comes after the verb ruikt and describes the subject.

After verbs like zijn, lijken, voelen, smaken, and ruiken, adjectives usually stay in their basic form:

• De schil is fris.
• De schil ruikt fris.

You use frisse when the adjective comes directly before a noun:

• de frisse geur
• een frisse sinaasappel
• de frisse schil

So here fris is correct.

Because maar is a coordinating conjunction, and after it you normally keep normal main-clause word order:

• maar ik eet die niet op

So the subject ik comes before the finite verb eet.

Dutch inversion happens after something else is put in first position:

• Morgen eet ik die niet op.
• Daarom eet ik die niet op.

But maar itself does not trigger inversion.

Die refers back to de schil.

Dutch often uses a demonstrative pronoun to avoid repeating the noun:

• De schil van een sinaasappel ruikt fris, maar ik eet die niet op.

Here die means something like that or that one, but in natural English it is often just translated as it.

It is die because schil is a de-word. If the earlier noun were a het-word, you would normally use dat instead.

Using die also adds a slight sense of contrast: the peel smells nice, but that is not something I eat.

Yes, that is grammatically possible, because schil is a de-word, and hem can refer back to many de-words.

However, for things, Dutch very often prefers die/dat, especially when referring back to something just mentioned or when there is some contrast or emphasis.

So:

• Ik eet die niet op. = very natural here
• Ik eet hem niet op. = possible, but a bit less natural in this context

For learners, die/dat is often the safer choice when referring back to an inanimate thing.

Because opeten is a separable verb.

The full verb is:

• opeten = to eat up / to finish eating

In a main clause, the finite verb moves to the usual verb position, and the particle op separates and goes to the end:

• Ik eet die op.
• Ik eet die niet op.

But in an infinitive or participle, the parts stay together:

• Ik wil die niet opeten.
• Ik heb die niet opgegeten.

This is a very common Dutch pattern.

Yes. Opeten usually means to eat up, to eat completely, or to finish eating something.

Compare:

• eten = to eat
• opeten = to eat up / finish

So:

• Ik eet die niet op literally means I do not eat it up

In this sentence, because the object is the peel, the natural English translation may simply be I don't eat it, even though Dutch uses opeten. The idea is that the peel may smell fresh, but it is not something the speaker consumes.

Because niet normally comes before the final verbal element in this kind of clause.

Since opeten splits into eet ... op, the negation goes before the final particle:

• Ik eet die op.
• Ik eet die niet op.

That is the normal Dutch placement. The sentence is negating the action opeten. So the structure is not random: niet appears before the part of the separable verb that has moved to the end.