После работы мне хочется поужинать дома.

Because после requires the genitive case.

• работа = the dictionary form, nominative
• after после, it changes to работы = genitive singular

So:

• после работы = after work
• literally: after of work

This is just a case pattern you need to memorize:

• после урока = after the lesson
• после фильма = after the movie
• после работы = after work

Both can mean something like I want, but they are not exactly the same in tone.

• я хочу = I want
• мне хочется = I feel like / I have a desire to

In this sentence, мне хочется sounds a bit softer, more natural for a passing feeling or urge.

Compare:

• Я хочу поужинать дома. = I want to have dinner at home.
• Мне хочется поужинать дома. = I feel like having dinner at home.

So мне хочется often expresses a more personal, internal feeling rather than a direct statement of will.

Хочется is from the verb хотеться, which is an impersonal verb.

That means Russian does not treat I as the grammatical subject here. Instead, the person experiencing the feeling appears in the dative case:

• мне хочется = I feel like...
• literally something like to me, it is wanted

This is why the sentence does not use я.

A useful pattern is:

• мне хочется спать = I feel sleepy / I feel like sleeping
• ему хочется есть = he feels like eating
• нам хочется отдохнуть = we feel like resting

Because with хочется, the person who experiences the desire is put in the dative.

So:

• я = I
• мне = to me

In this construction, Russian thinks of the feeling as happening to someone.

That is why:

• мне хочется = I feel like...
• тебе хочется = you feel like...
• ей хочется = she feels like...

This is very common with impersonal expressions in Russian.

Поужинать is the perfective form, while ужинать is imperfective.

Here, Russian uses поужинать because it means to have dinner once, as a complete event.

• ужинать = to be having dinner / to have dinner regularly
• поужинать = to have dinner once, to eat dinner and finish

In this sentence, the speaker feels like doing one completed action after work, so perfective is very natural:

• Мне хочется поужинать дома. = I feel like having dinner at home.

If you used ужинать, it would sound less natural here unless you meant the activity in a more general sense.

In this verb, по- helps create the perfective partner of ужинать.

So:

• ужинать = to dine / to have dinner
• поужинать = to have dinner, viewed as a completed action

This is a very common pattern with verbs connected to meals:

• завтракать → позавтракать = to have breakfast
• обедать → пообедать = to have lunch
• ужинать → поужинать = to have dinner

So the prefix is not really translating as a separate word like for a bit here; its main role is aspect.

Дома means at home.

This is an adverb, not the noun house in a normal case form.

Compare:

• дома = at home
• домой = home, toward home

So:

• Я ужинаю дома. = I have dinner at home.
• Я иду домой. = I am going home.

In your sentence, the speaker wants to have dinner at home, not go home, so дома is correct.

Because Russian does not need я here.

The idea I is already expressed by мне in the impersonal construction мне хочется.

So the sentence is understood as:

• После работы мне хочется поужинать дома.
• literally: After work, to me it feels desirable to have dinner at home.

In natural English, we just say After work, I feel like having dinner at home.

Russian often leaves out subject pronouns when the meaning is already clear.

Yes. Russian word order is fairly flexible, and changing it usually changes emphasis, not the basic meaning.

Your sentence:

• После работы мне хочется поужинать дома.

Possible variations:

• Мне хочется поужинать дома после работы.
• Дома мне хочется поужинать после работы.
• После работы дома мне хочется поужинать.

These versions all suggest roughly the same idea, but the focus shifts a little.

The original order sounds very natural because it starts with the time phrase после работы and then gives the main idea.

Yes, absolutely.

That sentence is correct and natural:

• Я хочу поужинать дома после работы.

The difference is mostly nuance:

• Я хочу... = more direct, straightforward
• Мне хочется... = softer, more like I feel like...

So both are good, but мне хочется often sounds a bit more idiomatic when talking about a spontaneous desire.

Yes, very close.

После работы can mean:

• after finishing work today
• after work, in the usual everyday sense

The exact meaning depends on context.

For example:

• После работы я иду домой. = After work, I go home / I’m going home after work.
• После работы мне хочется поужинать дома. = After work, I feel like having dinner at home.

So it works much like English after work.