На ужин я запеку рыбу с картофелем.

На ужин is the normal Russian way to say for dinner in the sense of as the dinner meal or for tonight’s dinner.

• На завтрак = for breakfast
• На обед = for lunch
• На ужин = for dinner

So На ужин я запеку рыбу с картофелем means something like For dinner, I’ll bake fish with potatoes.

Для ужина is possible in some contexts, but it sounds less natural here. It usually means for the purpose of dinner or intended for dinner, not the usual everyday way to introduce what someone will cook.

Запеку is the 1st person singular future of the perfective verb запечь.

Russian uses aspect very strongly:

• печь = to bake, be baking, bake in general (imperfective)
• запечь = to bake something completely / to bake as a single finished action (perfective)

Because the sentence talks about one future completed action, Russian uses the perfective future:

• я запеку = I will bake

If you said я пеку, that usually means I am baking or I bake in a habitual sense, not I will bake.

It suggests baking/roasting something in the oven as a completed cooking action.

So я запеку рыбу means:

• I’ll bake the fish
• I’ll roast the fish
• I’ll put the fish in the oven and cook it

The prefix за- here helps form a perfective verb. In many cases, it is best to learn запечь simply as the perfective partner of печь in cooking contexts.

Because рыбу is in the accusative case, which is used for the direct object.

The person is baking the fish, so fish is the thing directly affected by the action:

• рыба = nominative, dictionary form
• рыбу = accusative

This is the normal pattern for many feminine nouns ending in -а:

• книга → книгу
• мама → маму
• рыба → рыбу

So:

• Я запеку рыбу = I will bake fish

Because the preposition с meaning with requires the instrumental case.

• картофель = nominative
• с картофелем = with potatoes / with potato

So the pattern is:

• с рыбой = with fish
• с мясом = with meat
• с картофелем = with potatoes

This is one of the first big case patterns learners meet:
с + instrumental when it means with.

Russian often uses картофель as a mass noun, similar to potato in a general food sense.

So с картофелем can naturally mean:

• with potatoes
• with potato
• with some potato as a side ingredient

In everyday speech, many Russians would also say с картошкой, which is often more conversational and common.

So these can all be natural depending on context and style:

• с картофелем — a bit more neutral or formal
• с картошкой — more everyday and conversational

It can mean either, depending on context.

Most naturally, рыбу с картофелем suggests a dish of fish with potatoes, and very often that implies they are prepared together or served together as one meal.

Russian does not force a strict distinction here. If someone wanted to be more specific, they could say:

• запеку рыбу и картофель отдельно = I’ll bake the fish and potatoes separately
• запеку рыбу вместе с картофелем = I’ll bake the fish together with the potatoes

But in your sentence, the basic meaning is simply fish with potatoes.

Yes, it can be omitted.

Russian often drops personal pronouns when the verb ending already shows who is doing the action.

• Запеку рыбу с картофелем. = I’ll bake fish with potatoes.
• Я запеку рыбу с картофелем. = I’ll bake fish with potatoes.

Including я can add:

• emphasis
• contrast
• clarity
• a more explicit, complete sentence feel

So here я is not required, but it is completely natural.

Yes. Russian word order is flexible, and changing it changes the emphasis more than the core meaning.

Your sentence:

• На ужин я запеку рыбу с картофелем.

This puts На ужин first, so the sentence begins with the context for dinner.

Other possible orders:

• Я запеку рыбу с картофелем на ужин.
  More neutral in some contexts: I’ll bake fish with potatoes for dinner.

• Рыбу с картофелем я запеку на ужин.
  More emphasis on fish with potatoes.

• Запеку рыбу с картофелем на ужин.
  Natural if I is already understood.

So the original sentence is very natural, especially if the speaker is first setting the dinner plan.

Here рыбу usually means fish as food, not necessarily one whole fish animal.

In Russian, singular nouns are often used for food in a general sense:

• есть рыбу = to eat fish
• купить рыбу = to buy fish
• запечь рыбу = to bake fish

So рыбу here is best understood as some fish / a fish dish, not necessarily one fish in a biological sense.

The standard stress is:

На у́жин я запеку́ ры́бу с карто́фелем.

Breakdown:

• у́жин
• запеку́
• ры́бу
• карто́фелем

This is useful because stress in Russian is unpredictable and can change from form to form, so it is worth learning each word with stress.