Завтра я испеку пирог для друга.

Because испечь is a perfective verb, and perfective verbs form the future with a single word.

• испечь = to bake, to bake completely, to finish baking
• я испеку = I will bake

This is different from imperfective verbs, which use буду + infinitive for the future:

• я буду печь = I will be baking / I will bake (with focus on the process)
• я испеку = I will bake it and complete it

So in this sentence, испеку emphasizes a completed result: the pie will get baked.

The infinitive is испечь.

This verb is a little irregular, so the future forms do not look exactly like the infinitive. That is normal for some common Russian verbs.

A few forms are:

• я испеку
• ты испечёшь
• он/она испечёт
• мы испечём
• вы испечёте
• они испекут

So испеку is simply the 1st person singular future form of испечь.

It is in the accusative. The thing is that for many inanimate masculine singular nouns, the accusative looks exactly like the nominative.

• nominative: пирог
• accusative: пирог

So although the form stays the same, its role in the sentence is the direct object: I will bake a pie.

Compare that with an animate masculine noun, where accusative would usually match the genitive instead.

Because the preposition для requires the genitive case.

• друг = friend
• genitive singular: друга

So:

• для друга = for a friend / for my friend

This is a very common pattern in Russian:

• для мамы = for mom
• для брата = for a brother / for my brother
• для детей = for children

Yes, often it could.

Russian commonly uses the dative case for the person who receives or benefits from something:

• Я испеку другу пирог.

This is very natural and often sounds even more conversational than для друга.

The difference is roughly this:

• другу = to/for a friend, as the recipient or beneficiary
• для друга = for a friend, with a little more emphasis on purpose: the pie is intended for him

Both are understandable and correct in many contexts, but they are not always exactly identical in nuance.

Yes, it can often be omitted.

Russian verb endings usually show who the subject is. In испеку, the ending already tells us the subject is I.

So both are possible:

• Завтра я испеку пирог для друга.
• Завтра испеку пирог для друга.

The version with я may sound slightly more explicit or emphatic. Without я, it can sound a bit more natural in everyday speech if the subject is already clear from context.

Yes. Russian word order is more flexible than English word order because cases show grammatical roles.

All of these are possible, though the emphasis changes:

• Завтра я испеку пирог для друга.
• Я завтра испеку пирог для друга.
• Пирог для друга я испеку завтра.
• Для друга я завтра испеку пирог.

The original sentence is neutral and natural. Putting a word earlier often gives it more emphasis or makes it the topic of the sentence.

Завтра means tomorrow and functions as an adverb of time.

It tells you when the action will happen:

• Завтра я испеку пирог для друга. = Tomorrow I will bake a pie for a friend.

It is very common to place time words near the beginning of a Russian sentence, especially when setting the scene. But it can also move:

• Я завтра испеку пирог для друга.

Both are correct.

Not exactly.

• пирог is a pie or a baked pastry, often with filling
• торт is a cake, especially a layered or frosted cake

So испеку пирог means I’ll bake a pie, not necessarily a sweet cake. A пирог can be sweet or savory.

The standard stress is:

• За́втра
• испеку́
• пиро́г
• для дру́га

So the whole sentence is:

За́втра я испеку́ пиро́г для дру́га.

Stress matters in Russian, so it is worth learning words together with their stressed syllables.

It can mean either, depending on context.

Russian often does not use possessives like my as often as English does when the meaning is obvious.

So:

• для друга can mean for a friend
• or for my friend

If you want to make my explicit, you can say:

• для моего друга = for my friend

Without that, context decides the most natural translation.

Yes, it is natural and correct.

It is a clear, standard sentence with:

• a time expression: Завтра
• a subject: я
• a perfective future verb: испеку
• a direct object: пирог
• a phrase showing beneficiary/purpose: для друга

A very common conversational variant would be:

• Завтра испеку пирог другу.

But the original sentence is absolutely good Russian.