Після роботи я хочу повернутися додому.

Because після always requires the genitive case in Ukrainian.

The base form is робота (work), but after після it changes to роботи.

So:

• робота = nominative
• після роботи = after work / after the work

This is a very common pattern:

• після уроку = after the lesson
• після обіду = after lunch
• після зустрічі = after the meeting

Роботи is the genitive singular form of робота.

For feminine nouns ending in -а, the genitive singular is often formed by changing -а to -и:

• робота → роботи
• книга → книги
• машина → машини

So in this sentence, роботи does not mean plural. It is still singular: of work / after work.

Because повернутися means to return / to come back, while повернути usually means to turn or to return something.

The -ся makes the verb reflexive, and in this case it gives the meaning to return oneself, which English expresses simply as to return or to come back.

Compare:

• повернутися додому = to return home
• повернути ключ = to return the key
• повернути праворуч = to turn right

So in your sentence, повернутися is the correct choice because the subject is coming back himself/herself.

This is a question of aspect.

• повернутися = perfective
• повертатися = imperfective

In this sentence, я хочу повернутися додому means the speaker wants to complete one return home. That is a single, finished action, so the perfective verb fits well.

Use повертатися when you mean an ongoing, repeated, or habitual action:

• Я хочу повертатися додому раніше. = I want to be coming home earlier / I want to return home earlier regularly.

Use повернутися when you mean one completed return:

• Я хочу повернутися додому. = I want to return home.

Додому is a very common Ukrainian adverb meaning homeward / home.

So:

• йти додому = to go home
• повернутися додому = to return home
• їхати додому = to go home (by vehicle)

You may also see до дому, but додому is the normal, natural choice when talking about going home.

A helpful comparison:

• вдома = at home
• додому = to home / homeward

So:

• Я вдома. = I am at home.
• Я йду додому. = I am going home.

Yes. Ukrainian word order is more flexible than English word order.

The neutral order here is:

• Після роботи я хочу повернутися додому.

But other orders are possible for emphasis, for example:

• Я хочу повернутися додому після роботи.
• Додому я хочу повернутися після роботи.

These versions are all understandable, but they shift emphasis slightly.

The original sentence sounds natural and neutral, especially if після роботи is being used as the time frame at the beginning.

Yes, very often.

Because the verb form хочу already shows I want, Ukrainian often drops the subject pronoun when it is clear from context.

So both are possible:

• Після роботи я хочу повернутися додому.
• Після роботи хочу повернутися додому.

Including я can add clarity or emphasis. Omitting it often sounds more natural in everyday speech when the subject is obvious.

Because повернутися already contains the idea of coming back / returning.

English often uses phrases like go back, but Ukrainian can express that idea with a single verb:

• повернутися = to return / to come back / to go back

Then додому adds the destination:

• повернутися додому = return home

So you do not need another verb meaning go here.

Yes. This is a standard Ukrainian pattern:

• хотіти
  • infinitive

So:

• я хочу спати = I want to sleep
• я хочу їсти = I want to eat
• я хочу повернутися = I want to return

This is very similar to English want + to + verb, except Ukrainian uses the infinitive directly, without a separate word like to.

In standard pronunciation, -ся is usually pronounced lightly, roughly like sya, though in fast speech it may sound a bit reduced.

A learner-friendly breakdown is:

• по-вер-ну-ти-ся

The stress is on ну:

• повернУтися

So the whole word is approximately:

• po-ver-NOO-ty-sya

Even if your pronunciation is not perfect at first, the important thing is to keep the reflexive ending -ся, because it changes the meaning of the verb.