Learn Hardcore French: Paul mange un yaourt après le dîner.

Un yaourt = one yogurt (a single container/unit).
Du yaourt = some yogurt (an unspecified amount, mass). Both are correct; choose based on whether you mean one pot or an unspecified quantity.

Is yaourt masculine or feminine? What’s the plural?

Yaourt is masculine: un yaourt, le yaourt.
Plural: des yaourts. In speech, the plural -s is silent.

How do you pronounce the whole sentence?

Approximate IPA: [pɔl mɑ̃ʒ œ̃ ja.uʁ(t) apʁɛ lə dine]

Paul [pɔl]
mange [mɑ̃ʒ] (nasal vowel + the sound of s in “measure”)
un [œ̃] (nasal vowel)
yaourt [ja.uʁ] (final -t often silent; [ja.uʁt] also heard)
après [apʁɛ]
le [lə]
dîner [dine]

Does the French present mean both “eats” and “is eating”?

Yes. Paul mange can mean “Paul eats” (habitually) or “Paul is eating” (right now). Context decides.

Why is it après le dîner and not après du dîner?

After the preposition après, you use a straightforward noun phrase with the appropriate article: après le dîner, après la réunion, etc.
Après du dîner is incorrect here.
Note: après dîner (without article) also exists and is a bit more formal/literary; both are fine.

Can I move the time phrase to the front?

Yes: Après le dîner, Paul mange un yaourt.
Fronting the time phrase adds emphasis on when it happens. Use a comma after the fronted phrase.

How do I make it negative?

General negation (no yogurt at all): Paul ne mange pas de yaourt après le dîner.
With a pronoun: Paul n’en mange pas après le dîner.
To insist “not even one”: Paul ne mange pas un seul yaourt / pas un yaourt après le dîner.

How do I ask a yes/no question with this sentence?

Intonation (informal): Paul mange un yaourt après le dîner ?
Est-ce que (neutral): Est-ce que Paul mange un yaourt après le dîner ?
Inversion (formal): Paul mange-t-il un yaourt après le dîner ?

How do I replace un yaourt with a pronoun?

Use en. Because the noun is introduced by an indefinite article, keep the quantity:

Paul en mange un après le dîner. In negation: Paul n’en mange pas (après le dîner).

Could I use other verbs like prendre or dîner?

Prendre (to have): Paul prend un yaourt après le dîner is fine and natural.
Verb dîner (to have dinner): Après avoir dîné, Paul mange un yaourt.
To state the meal: Paul dîne = Paul is having dinner.

Does dîner always mean “dinner” across the Francophone world?

No.

In France: déjeuner = lunch, dîner = dinner.
In Belgium, Switzerland, Quebec: dîner = lunch, souper = dinner.
So in Quebec you’d likely hear: après le souper.

Any spelling or accent points to watch?

après has a grave accent on è.
dîner traditionally has a circumflex (î). The 1990 reforms allow diner, but dîner is still very common.
yaourt is standard; yogourt is common in Canada; yoghourt is dated.

Are there any liaisons or elisions to make here?

No required liaison in après le dîner (next word starts with consonant).
No liaison in mange un (there’s no latent consonant to link). You’ll just flow the sounds together (enchaînement).
Examples where you would liaise: après un film → [apʁɛ‿zœ̃ film]; après l’école (elision) → the le becomes l’.

How do I talk about more than one yogurt or quantities?

Plural: Paul mange deux yaourts / des yaourts.
With quantity words: beaucoup de yaourt, un peu de yaourt, trop de yaourt (note: after quantity words, use de, not des).

Why is the g in mange pronounced like the s in “measure”?

French g is “soft” ([ʒ]) before e/i/y. The spelling -ge- keeps it soft.
That’s why we write nous mangeons (with an extra e) to preserve the soft g before -ons.