La melodía de esa canción es muy relajante.

Because melodía is a feminine noun, so it takes the feminine article la.

A useful pattern is that many nouns ending in -ía are feminine:

• la melodía
• la idea
• la energía

So the article has to agree with the noun’s gender.

De here means of: the melody of that song.

So the structure is:

• la melodía = the melody
• de esa canción = of that song

This is a very common Spanish way to connect two nouns. English often also uses possession in other ways, such as that song’s melody, but Spanish normally uses de here.

Esa means that.

It is esa because it has to agree with canción, which is feminine singular:

• esta canción = this song
• esa canción = that song
• aquella canción = that song over there / that more distant song

So esa matches canción, not melodía.

The accent mark shows where the stress goes: can-CIÓN.

Without the written accent, Spanish stress rules would make you pronounce it differently. Since words ending in -n, -s, or a vowel are normally stressed on the second-to-last syllable, the accent is needed to show that canción is stressed on the last syllable.

The accent in melodía shows that the stress falls on -dí-: me-lo-DÍ-a.

It also helps show that í-a is pronounced in two syllables, not merged together. So melodía has four syllables:

• me
• lo
• dí
• a

We use es because the sentence describes a characteristic of the melody: it is relaxing.

In Spanish, ser is often used for descriptions, identity, and more permanent or defining qualities:

• La melodía es relajante.

Estar is more often used for states or conditions:

• Estoy relajado. = I am relaxed.

So:

• relajante = relaxing, something that causes relaxation
• relajado/a = relaxed, how someone feels

Because relajante means relaxing, not relaxed.

That is an important difference:

• relajante = something causes relaxation
• relajado / relajada = someone or something is in a relaxed state

So in this sentence, the melody produces that effect, which is why relajante is the natural choice.

It actually already agrees correctly. Some adjectives in Spanish have the same form for masculine and feminine in the singular, and relajante is one of them.

Compare:

• un sonido relajante
• una melodía relajante

The adjective only changes in the plural:

• sonidos relajantes
• melodías relajantes

Because muy is used before adjectives and adverbs:

• muy relajante = very relaxing

Mucho is usually used with nouns or as a pronoun/adverb in other structures:

• mucha música = a lot of music
• me gusta mucho = I like it a lot

So before relajante, you need muy.

Yes, you could, but it means something slightly different.

• La melodía de esa canción es muy relajante.
  This focuses specifically on the melody.
• La canción es muy relajante.
  This refers to the whole song.

So the original sentence is more precise.

Yes. That is also completely natural.

It means:

• That song has a very relaxing melody.

The difference is mostly in structure:

• La melodía de esa canción es muy relajante = more directly about the melody
• Esa canción tiene una melodía muy relajante = more directly about the song having that quality

Both are good Spanish.

No. De only contracts with el:

• de + el = del

For example:

• el sonido del piano

But with esa, there is no contraction:

• de esa canción

So de esa stays exactly as it is.

A careful pronunciation would be roughly:

la me-lo-DI-a de E-sa can-CIÓN es muy re-la-JAN-te

A couple of useful notes:

• melodía is stressed on dí
• canción is stressed on ción
• in much of Spain, the ci in canción is pronounced with a th sound, roughly can-THYON
• j in relajante is a strong throat sound

So in much of Spain, relajante sounds roughly like re-la-HAN-te.