Ta melodia pomaga mi odpocząć po pracy.

No. Polish does not have articles like a/an and the.

Ta is a demonstrative word, meaning this (and sometimes that, depending on context). So ta melodia is more literally this melody / this tune, not just the melody.

If you only wanted to say melody in a general way, you could often just say melodia without any article-like word.

Because melodia is a feminine singular noun in the nominative case, and the demonstrative has to agree with it.

The Polish word behind ta is part of the set:

• ten for masculine
• ta for feminine
• to for neuter

So:

• ten dom = this house
• ta melodia = this melody
• to okno = this window

Since melodia is feminine, ta is the correct form.

Here is the breakdown:

• Ta melodia — nominative
  This is the subject of the sentence: the thing doing the helping.

• mi — dative
  This means to me / for me. The verb pomagać normally takes the person helped in the dative.

• odpocząć — infinitive
  Infinitives do not have case.

• po pracy — locative after the preposition po
  The basic noun is praca. After po, it changes to pracy.

So the structure is basically:

[subject] + helps + [to me] + [infinitive] + [after work]

Pomaga is the 3rd person singular present tense form of pomagać (to help).

Why 3rd person singular? Because the subject is ta melodia = this melody, which is singular.

A few forms of pomagać are:

• ja pomagam = I help
• ty pomagasz = you help
• on/ona/ono pomaga = he/she/it helps

So Ta melodia pomaga... means This melody helps...

Both mi and mnie can mean me, but here mi is the normal, unstressed form.

With pomagać, Polish uses the dative:

• pomagać komu? = to help whom?

So:

• mi = to me
• ci = to you
• mu = to him
• jej = to her

Mnie is also possible, but it usually sounds more emphatic or contrastive:

• Ta melodia pomaga mnie, nie tobie. = This melody helps me, not you.

In a neutral sentence, mi is the natural choice.

Because in Polish, the infinitive already includes the meaning of English to + verb.

So:

• odpocząć = to rest / to relax
• pomagać = to help
• pracować = to work

Polish does not need a separate word like English to before an infinitive.

That means:

• pomaga mi odpocząć = helps me rest / helps me to relax

This is a question of aspect, which is very important in Polish.

• odpoczywać = imperfective
  focuses on the process, ongoing action, or repeated action of resting

• odpocząć = perfective
  focuses more on the result: getting some rest, managing to relax, becoming rested

In this sentence, odpocząć sounds very natural because the idea is that the melody helps you unwind after work and reach a restful state.

Very roughly:

• pomaga mi odpocząć = helps me relax / helps me get some rest
• pomaga mi odpoczywać = helps me be in the process of resting

The second one is not impossible, but odpocząć is the more idiomatic choice here.

Because po here means after, and in this kind of time expression it takes the locative case.

The noun is:

• praca = work

Its locative singular form is:

• pracy

So:

• po pracy = after work

You can see the same pattern in:

• po obiedzie = after dinner
• po szkole = after school
• po treningu = after training

Yes. Polish word order is much more flexible than English word order, because cases help show what each word is doing.

The given sentence is a neutral, natural order:

Ta melodia pomaga mi odpocząć po pracy.

But you could also say:

• Po pracy ta melodia pomaga mi odpocząć.
  This emphasizes after work.

• Ta melodia mi pomaga odpocząć po pracy.
  Also natural, a bit more conversational.

• Mi ta melodia pomaga odpocząć po pracy.
  This gives extra emphasis to me.

So the meaning stays similar, but the focus changes.

Yes, depending on what you mean.

• melodia = melody, tune
• muzyka = music
• piosenka = song

So:

• Ta melodia pomaga mi odpocząć po pracy.
  This tune/melody helps me relax after work.

• Ta muzyka pomaga mi odpocząć po pracy.
  This music helps me relax after work.

• Ta piosenka pomaga mi odpocząć po pracy.
  This song helps me relax after work.

If you mean the overall music you are listening to, muzyka is often the most natural choice. If you mean a specific tune, melodia fits well.