После работы мне хочется немного полежать.

Because после requires the genitive case.

The noun работа is nominative singular.
Its genitive singular form is работы.

So:

• работа = work, job
• после работы = after work

This is a very common pattern in Russian:

• после урока = after the lesson
• после обеда = after lunch
• после фильма = after the film

Literally, it is something like to me it is wanted or I feel like.

Russian often expresses feelings and states with:

• a person in the dative case
• plus an impersonal verb

So:

• мне = to me
• хочется = one feels like, is inclined to want

Together, мне хочется means:

• I feel like
• I want to
• I have a desire to

In this sentence, it sounds softer and more natural than a direct я хочу.

Because the construction хочется takes the experiencer in the dative case, not the nominative.

Compare:

• я хочу = I want
• мне хочется = I feel like / I kind of want to

So мне is not the subject in the English sense. It means to me.

This pattern is common with words for physical or emotional states:

• мне холодно = I am cold
• мне грустно = I am sad
• мне хочется спать = I feel sleepy / I want to sleep

Both can translate as I want, but they are not exactly the same.

• я хочу = a more direct, definite statement of desire
• мне хочется = softer, more personal, more like I feel like

In this sentence, мне хочется немного полежать sounds natural because it expresses a temporary feeling after work.

Compare:

• Я хочу домой. = I want to go home.
• Мне хочется домой. = I feel like going home.

The second one often sounds less forceful and more emotional.

Полежать means to lie down for a while or to have a short lie-down.

It is formed from лежать with the prefix по-, which often gives the idea of doing something for a limited time.

So:

• лежать = to be lying / to lie
• полежать = to lie down for a bit

That fits very well with немного:

• немного полежать = to lie down for a little while

Using лежать here would sound less natural if you mean a short period of rest.

Mostly lie for a while.

English lie down can focus on the movement from sitting/standing to a lying position. Russian полежать usually focuses more on spending some time lying down, not on the movement itself.

If you want to emphasize the action of getting into a lying position, Russian often uses лечь:

• лечь = to lie down, to get into bed
• лежать = to be lying
• полежать = to lie/rest for a while

So in this sentence, полежать suggests a short rest after work.

Because хочется expresses a desire, and Russian usually follows that with the verb for the desired action in the infinitive.

So:

• хочется полежать = feel like lying down
• хочется поесть = feel like eating
• хочется поспать = feel like sleeping

This is very similar to English want to + verb or feel like + -ing.

Немного means a little, a bit, or for a little while.

In this sentence it modifies полежать:

• немного полежать = to lie down for a bit

It makes the idea sound lighter and more casual. Without it, the sentence would still be correct:

• После работы мне хочется полежать.

But немного adds the sense that the speaker only wants a short rest.

Yes. Russian word order is flexible, and the basic meaning stays the same.

For example, you could also say:

• Мне после работы хочется немного полежать.
• После работы хочется немного полежать.
• Немного полежать после работы мне хочется.

However, the original order sounds very natural and neutral:

• После работы мне хочется немного полежать.

It starts with the time phrase after work, then gives the feeling, then the action.

Usually it means after work, in the ordinary everyday sense: after the working day, after you are done working.

It does not have to emphasize the exact moment of finishing. It is just the normal time period following work.

So the sentence suggests something like:

• once work is over
• when I get home from work
• after the workday, I feel like lying down for a bit

The main stresses are:

• пОсле
• рабОты
• мне
• хОчется
• немнОго
• полежАть

So the sentence is pronounced approximately as:

ПОсле рабОты мне хОчется немнОго полежАть.

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