Je mange du riz au lait après le dîner.

Because du is a partitive article. In French, when you talk about an unspecified amount of food, drink, or another uncountable thing, you usually need a partitive article.

So:

• Je mange du riz au lait = I am eating some rice pudding.
• Je mange le riz au lait would mean the rice pudding, probably a specific one already known in the conversation.

French often requires an article where English may not.

Du is the form of the partitive article used before a masculine singular noun.

It is historically made from:

• de + le = du

In this sentence, it does not really mean of the in a natural English sense. It simply marks some or an unspecified quantity of.

Other partitive forms are:

• de la
• de l’
• des

Examples:

• du pain
• de la soupe
• de l’eau
• des légumes

Because riz au lait is the normal French name of the dish.

French often uses à / au / aux in names of foods to show what they are made with or flavored with:

• café au lait
• glace à la vanille
• tarte aux pommes

So riz au lait is the standard expression, not just a literal description like rice with milk. It functions as the name of a dessert.

Au is a contraction of:

• à + le = au

Since lait is a masculine singular noun, French uses au here.

Compare:

• au chocolat = with chocolate / chocolate-flavored
• à la crème = with cream
• aux amandes = with almonds

So riz au lait literally looks like rice in the style of milk / with milk, but in real usage it is simply the set expression for the dish.

Yes. Riz au lait is a fixed food name, like rice pudding in English.

Even though it has several words, French speakers understand it as one dish. That is why du applies to the whole expression:

• du riz au lait

not separately to riz and lait.

Because French often uses the definite article with meals:

• le petit-déjeuner
• le déjeuner
• le dîner

So after a preposition, you normally keep the article:

• avant le dîner
• après le dîner
• pendant le dîner

In English, we often say just after dinner, but French usually says après le dîner.

Usually yes in modern standard French, but there is some regional variation.

In much of France:

• petit-déjeuner = breakfast
• déjeuner = lunch
• dîner = dinner

But in some French-speaking regions, especially depending on country or local usage, dîner can sometimes refer to a different meal. So the exact meal name can vary by region, even though the grammar stays the same.

Yes. French is flexible here.

You can say:

• Je mange du riz au lait après le dîner.
• Après le dîner, je mange du riz au lait.

Both are correct.

The version with après le dîner at the end sounds very natural and neutral. Putting it first gives a little more emphasis to the time.

In a basic negative sentence, du usually changes to de (or d’ before a vowel sound).

So:

• Je mange du riz au lait. becomes
• Je ne mange pas de riz au lait.

This is a very common French pattern:

• Je bois du café → Je ne bois pas de café
• Il mange de la soupe → Il ne mange pas de soupe

They mostly help with spelling and pronunciation.

• In après, the grave accent in è shows an open eh sound.
• In dîner, the circumflex on î does not usually create a big pronunciation difference for most learners, but it is part of the correct spelling.

So the accents are important to write correctly, even if one of them does not strongly change the sound in everyday speech.

Yes, that is possible.

• Je mange du riz au lait focuses on the action of eating.
• Je prends du riz au lait can sound a little broader, like I have / I take some rice pudding.

For food, manger is the most direct and obvious verb, so it is a very good choice here.