Завтра я сдам лабораторную по физике и потом пойду домой.

Russian has two different ways to talk about the future:

• Imperfective future: буду
  • infinitive
    Example: буду сдавать, буду идти
• Perfective future: a single conjugated verb
  Example: сдам, пойду

In this sentence, both verbs are perfective, because they describe completed, one-time actions in sequence:

• сдам = I will hand in / complete
• пойду = I will go / set off

So Завтра я сдам... и потом пойду... sounds like Tomorrow I’ll do X, and then I’ll do Y.

If you used imperfective forms here, the meaning would change and sound more like process, repetition, or general future activity rather than two completed next steps.

In everyday Russian, лабораторную is short for лабораторную работу.

So the full phrase would be:

• сдать лабораторную работу = to hand in / complete a lab assignment

Russian often drops the noun when it is obvious from context. This is very common in speech and informal writing.

So:

• лабораторную really means the lab assignment / lab report / lab work, depending on context.

Grammatically, it is the feminine accusative singular form, because the omitted noun работа is feminine and the phrase is the direct object of сдам.

Because it is the direct object of сдам, so it takes the accusative case.

The hidden full phrase is:

• nominative: лабораторная работа
• accusative: лабораторную работу

Since работу is omitted, only the adjective remains, but it still keeps the accusative feminine singular ending:

• лабораторная → nominative
• лабораторную → accusative

So the form tells you what role the word is playing in the sentence.

Here по means in / on / for the subject of, and with that meaning it takes the dative case.

So:

• физика = physics
• по физике = for physics / in physics / on physics

This is a very common Russian pattern for school and university subjects:

• экзамен по математике = exam in math
• книга по истории = book on history
• задание по русскому = assignment for Russian

So лабораторная по физике means a physics lab assignment.

Сдать is a very broad verb, and its exact meaning depends on context. It can mean things like:

• hand in / submit
• take and pass
• turn over
• rent out

In this sentence, with лабораторную, the most likely meaning is something like:

• hand in the lab assignment
• successfully complete the lab
• sometimes even pass/check off the lab requirement

In student contexts, сдать лабораторную often means you completed it and got it accepted by the teacher.

So yes, сдать can be tricky because the English translation changes with context.

Пойду is perfective and means I will go / I will set off. It focuses on the start or single occurrence of the movement.

That works well here because the sentence describes the next action after finishing the lab:

• first I’ll hand in the lab
• then I’ll go home

By contrast, иду is present tense and usually means I am going / I go.

So:

• потом пойду домой = then I’ll go home
• потом иду домой would usually not fit this future sequence

Russian commonly uses пойти for a planned future action of setting off somewhere.

Домой means home, specifically toward home / to home. It is an adverb, not a noun phrase.

So:

• идти домой = to go home

This is the normal way to say it in Russian.

Compare:

• в дом = into a house/building
• к дому = toward the house / to the house

If you mean home in the personal sense, Russian usually uses:

• домой for motion toward home
• дома for being at home

Examples:

• Я иду домой. = I’m going home.
• Я дома. = I’m at home.

Russian word order is flexible, and putting завтра first is very natural because it sets the time frame right away.

So Завтра at the front means something like:

• As for tomorrow...
• Tomorrow, ...

This is common when the speaker wants to establish the time before giving the actions.

You could also say:

• Я завтра сдам лабораторную...

That is also correct. The difference is mostly about emphasis and flow, not basic meaning.

Yes, it could be omitted.

Russian often leaves out subject pronouns when the verb ending already makes the subject clear:

• Завтра сдам лабораторную по физике и потом пойду домой.

This still clearly means I because сдам and пойду are first-person singular.

Including я can make the sentence:

• slightly clearer in isolation
• a bit more emphatic
• more natural in some contexts, especially for learners or when contrasting with someone else

So both versions are correct.

It is not wrong, but it is a little emphatic.

• и = and
• потом = then / afterward

Together, и потом makes the sequence very explicit:

• and then

You could say:

• Завтра я сдам лабораторную по физике, потом пойду домой.
• Завтра я сдам лабораторную по физике и пойду домой.
• Завтра я сдам лабораторную по физике и потом пойду домой.

All are possible. The version with и потом highlights the order most clearly.

You could, but the meaning would change.

This sentence uses perfective verbs because it presents a chain of completed future events:

• сдам = I’ll hand it in / complete it
• пойду = I’ll go / set off

If you say буду сдавать, that suggests process or ongoing activity:

• Tomorrow I’ll be working on handing in / taking / dealing with the lab

And буду идти домой sounds like:

• I’ll be walking home
  rather than
• I’ll go home

So for a simple plan with one action followed by another, the perfective forms сдам and пойду are the natural choice.