После ужина я съел дольку мандарина.

Because после requires the genitive case.

• ужин = dinner
• ужина = of dinner / after dinner

So:

• после ужина = after dinner

This is a fixed grammar pattern:

• после работы = after work
• после урока = after the lesson
• после фильма = after the film

Съел is the past tense, masculine singular, perfective form of съесть.

• есть / ел = to eat / was eating, ate in an ongoing or general sense
• съесть / съел = to eat up, finish eating, consume completely

In this sentence, съел shows a completed action: the speaker ate the segment.

Compare:

• Я ел мандарин. = I was eating / I ate a mandarin
• Я съел мандарин. = I ate up a mandarin / finished eating it

So съел is used because the action is presented as completed.

The verb agrees with the subject in the past tense.

Here the subject is я, but Russian past tense also shows the speaker’s gender:

• я съел = I ate up, if the speaker is male
• я съела = I ate up, if the speaker is female

Other forms:

• мы съели = we ate up
• он съел = he ate up
• она съела = she ate up

So съел tells you the speaker is male.

Because it is the direct object of the verb съел, so it goes into the accusative case.

• dictionary form: долька = segment, slice
• accusative singular: дольку

This is a very common pattern for feminine nouns ending in -а:

• книга → книгу
• лампа → лампу
• долька → дольку

So:

• Я съел дольку = I ate a segment

Долька means a segment or wedge, especially of a citrus fruit.

For example:

• долька апельсина = an orange segment
• долька лимона = a lemon wedge
• долька мандарина = a mandarin segment

So the sentence is not saying the speaker ate the whole fruit, but one segment of it.

Because мандарина is in the genitive case after a noun meaning a part of something.

This is a very common Russian structure:

• кусок хлеба = a piece of bread
• чашка чая = a cup of tea
• бутылка воды = a bottle of water
• долька мандарина = a segment of a mandarin

So:

• долька = segment
• мандарина = of a mandarin

This is often called the genitive of content or whole-to-part relationship.

Not really. Долька is a fairly specific unit: a single segment.

If you wanted to say part of a mandarin more vaguely, Russian would use something else, for example:

• кусочек мандарина = a little piece of mandarin
• часть мандарина = part of a mandarin

So дольку мандарина specifically suggests one citrus segment.

Yes, Russian often omits subject pronouns when they are clear from the verb form or context.

So both are possible:

• После ужина я съел дольку мандарина.
• После ужина съел дольку мандарина.

Including я can:

• add emphasis
• make the sentence clearer in isolation
• contrast with someone else

So я is natural here, but not strictly necessary.

Yes, Russian word order is relatively flexible.

This sentence starts with После ужина to set the time frame first:

• После ужина я съел дольку мандарина. = After dinner, I ate a mandarin segment.

Other possible orders:

• Я съел дольку мандарина после ужина.
• Дольку мандарина я съел после ужина.

These all mean roughly the same thing, but the focus changes slightly.

• После ужина... emphasizes when
• Я съел... is more neutral
• Дольку мандарина я съел... emphasizes what was eaten

Russian has no articles like English a/an/the.

So:

• дольку can mean a segment or the segment
• мандарина can mean of a mandarin or sometimes of the mandarin, depending on context

Russian relies on:

• context
• word order
• stress/emphasis
• sometimes extra words like этот = this

So the sentence is natural without any article.

Yes.

• dictionary form: мандарин = mandarin, tangerine
• мандарина here is the genitive singular

In this sentence it appears in the genitive because it depends on долька:

• долька чего? = a segment of what?
• мандарина

So мандарина is not a different word, just a different grammatical form of мандарин.

That would sound unnatural in this context.

Russian normally says:

• долька мандарина

Using от would usually suggest separation from something in a less natural way here. For fruit segments, the normal expression is simply the noun + genitive pattern:

• долька апельсина
• долька лимона
• долька мандарина

So дольку мандарина is the standard phrasing.

A few examples:

• После ужина я съела дольку мандарина.
  A female speaker: I ate a segment of mandarin after dinner.

• После ужина я съел две дольки мандарина.
  A male speaker: I ate two mandarin segments after dinner.

• После ужина я съела две дольки мандарина.
  A female speaker, two segments

Notice:

• съел / съела changes with the speaker’s gender
• after две, долька becomes дольки
• мандарина stays in the genitive singular here

Yes, it is completely natural.

It sounds like normal spoken or written Russian:

• После ужина = a common time expression
• съел = natural perfective verb for a completed act of eating
• дольку мандарина = standard way to say a mandarin segment

So this is a good example of everyday, idiomatic Russian.