Po pracy nie chcę się już niczym martwić, tylko spokojnie wypić herbatę.

Po pracy means after work.

The preposition po often takes the locative case when it means after in time expressions.
So:

• praca = work
• po pracy = after work

This is a very common pattern in Polish:

• po szkole = after school
• po obiedzie = after lunch
• po spotkaniu = after the meeting

Chcę is the 1st person singular form of chcieć (to want).

So:

• chcę = I want
• nie chcę = I don’t want

Polish often leaves out the subject pronoun ja because the verb ending already shows who is doing the action. So:

• (Ja) nie chcę = I don’t want

Because martwić się is the normal verb meaning to worry or to be worried.

Without się, martwić usually means to worry someone or to cause worry, not to worry oneself in the everyday sense.

Compare:

• martwić się = to worry
• To mnie martwi. = That worries me.

So in this sentence, nie chcę się martwić means I don’t want to worry.

In Polish, się is very flexible in position. It usually does not go at the beginning of a clause, and it often appears early in the sentence.

So these are both possible:

• Nie chcę się już niczym martwić
• Nie chcę już niczym się martwić

The version in your sentence sounds natural and common. Word order with się is often about rhythm and style more than a big change in meaning.

Here już means something like any longer / anymore / now depending on context.

In this sentence:

• nie chcę się już niczym martwić
  = I don’t want to worry about anything anymore

So już suggests a change of state: up to now there may have been stress or worry, but after work the speaker wants that to stop.

Because martwić się takes a phrase with czymś (about something), and that requires the instrumental case.

Pattern:

• martwić się czymś = to worry about something

So:

• czymś = about something
• niczym = about nothing / anything (in a negative sentence)

Because the sentence is negative (nie chcę), Polish uses double negation:

• nie chcę się niczym martwić
  literally: I don’t want to worry myself with nothing
  natural English: I don’t want to worry about anything

This is normal in Polish.

Polish normally uses negative concord, which means multiple negative words appear together in one negative sentence.

So English says:

• I don’t want to worry about anything

But Polish says:

• Nie chcę się niczym martwić

You will often see this pattern:

• nie ... nic = not ... anything / nothing
• nie ... nigdy = not ... ever / never
• nie ... nikt = not ... anyone / nobody
• nie ... nigdzie = not ... anywhere / nowhere

This is one of the biggest differences from English.

Here tylko means just, only, or but rather.

The structure is:

• nie chcę X, tylko Y

This means:

• I don’t want X, only/rather Y
• more naturally: I don’t want to do X, I just want to do Y

So:

• Po pracy nie chcę się już niczym martwić, tylko spokojnie wypić herbatę.
• After work I don’t want to worry about anything anymore, I just want to quietly drink a cup of tea.

Wypić is the perfective form of to drink, meaning to drink up / finish drinking / have a drink as a completed action.

• pić = to drink (imperfective)
• wypić = to drink up, to drink completely, to have as a finished act (perfective)

In this sentence, the speaker imagines one complete, calm action after work: have a cup of tea. That is why wypić fits well.

If you used pić, it would focus more on the process or activity rather than the completed act.

Spokojnie is an adverb from spokojny (calm, peaceful).

Here it means:

• calmly
• peacefully
• in peace

So:

• spokojnie wypić herbatę = to drink tea peacefully / quietly / in peace

It describes how the person wants to drink the tea.

Herbatę is the accusative singular form of herbata (tea).

It is in the accusative because it is the direct object of wypić.

• herbata = tea
• wypić herbatę = to drink tea / to drink a cup of tea

This is very common with transitive verbs in Polish.

In natural usage, wypić herbatę often implies have/drink a tea or drink a cup of tea, even though cup is not stated.

Polish often leaves such things understood from context. So the phrase sounds very natural and idiomatic.

If someone wanted to be more explicit, they could say:

• wypić filiżankę herbaty = drink a cup of tea

But wypić herbatę is completely normal.

Yes. Polish word order is fairly flexible, though some versions sound more natural than others.

For example, you could also hear:

• Po pracy już nie chcę się niczym martwić, tylko spokojnie wypić herbatę.
• Nie chcę po pracy już się niczym martwić, tylko spokojnie wypić herbatę.

The original sentence sounds natural and smooth. The word order helps give a relaxed, conversational feeling.

In Polish, changing word order often changes emphasis rather than basic meaning.

Because Polish usually drops subject pronouns when the verb form already makes the subject clear.

• chcę already means I want

So ja is unnecessary unless you want emphasis or contrast:

• Ja nie chcę się martwić, ale on chce wszystko kontrolować.
  = I don’t want to worry, but he wants to control everything.

In your sentence, no special emphasis is needed, so leaving out ja is the most natural choice.