Los documentales de naturaleza me ayudan a relajarme después del trabajo.

Because the subject (los documentales de naturaleza) is plural.

• ayuda = he/she/it helps (singular)
• ayudan = they help (plural)

In the sentence:

• Subject: Los documentales de naturaleza → they
• Verb: ayudan
• Pronoun: me (who is being helped)

So it literally means: “Nature documentaries help me…”, and since documentaries is plural, you need ayudan.

Me is an indirect object pronoun meaning “to me” or “me”.

• ayudar a alguien = to help someone
• me ayudan = they help me

You could expand it (less natural, more emphatic) as:

• Los documentales de naturaleza me ayudan a mí…
  (“Nature documentaries help me…”)

In normal speech, you just use me before the verb.

With ayudar followed by another verb in the infinitive, Spanish normally uses the preposition a:

• ayudar a + infinitive
  • Me ayudan a estudiar. – They help me (to) study.
  • Me ayuda a concentrarme. – It helps me (to) concentrate.

So you say:

• me ayudan a relajarme
  not
• me ayudan relajarme (incorrect)

Because in Spanish, when you talk about you yourself relaxing, you usually use the reflexive verb relajarse:

• relajar (non‑reflexive) = to relax something/someone else
  • La música relaja a los bebés. – Music relaxes babies.
• relajarse (reflexive) = to relax oneself
  • Quiero relajarme. – I want to relax (myself).

In the sentence, you are the one who gets relaxed, so:

• a relajarme = “to relax myself / to relax” (myself is implicit)

Grammatically:

• infinitive: relajarse
• attach pronoun: relajar + me → relajarme

Yes, but the meaning changes slightly.

• Me relajan los documentales de naturaleza.
  = Nature documentaries relax me (they directly cause you to feel relaxed).

• Los documentales de naturaleza me ayudan a relajarme.
  = Nature documentaries help me relax (they make it easier for you to relax, they contribute to it).

Both are correct; me relajan is shorter and more direct, me ayudan a relajarme emphasizes the idea of helping you to relax.

Because in Spanish, when you use después de with a noun, you usually include the article:

• después del trabajo = after the work / after work
• después de la cena = after the dinner
• después del partido = after the game

del is just the contraction of:

• de + el = del

So:

• después + de + el trabajo → después del trabajo

Después de trabajo sounds unnatural or incomplete in this context.

Yes, and both are common, but there is a small difference in focus:

• después del trabajo
  Focuses on the period of work as a thing, like “after work (the workday)”.

• después de trabajar
  Uses a verb and focuses on the action: “after working”.

Both would be natural:

• Los documentales de naturaleza me ayudan a relajarme después del trabajo.
• Los documentales de naturaleza me ayudan a relajarme después de trabajar.

Both are possible, but there’s a nuance:

• documentales de naturaleza
  = nature documentaries (a general category, “about nature” in a broad way).
  Very natural and common.

• documentales de la naturaleza
  = documentaries of the nature / of nature itself, a bit more specific or literary, as if nature is almost a character or subject itself.

In everyday speech, documentales de naturaleza is shorter and more typical for “nature documentaries” as a genre.

Documentales naturales would mean something like “natural documentaries,” which sounds odd in Spanish and doesn’t clearly mean “about nature.”

Spanish usually expresses “X documentaries” (documentaries about X) as:

• documentales de historia – history documentaries
• documentales de ciencia – science documentaries
• documentales de crimen – crime documentaries
• documentales de naturaleza – nature documentaries

So de + noun is the normal pattern, not using naturales as an adjective here.

Yes, Spanish word order is more flexible than English. These are all grammatically correct:

1. Los documentales de naturaleza me ayudan a relajarme después del trabajo.
   (Most neutral and common.)

2. Me ayudan los documentales de naturaleza a relajarme después del trabajo.
   Puts a bit more focus on they help me at the beginning.

3. Los documentales de naturaleza, después del trabajo, me ayudan a relajarme.
   With commas, more stylistic, like in written or careful speech.

Meaning stays the same; you just change emphasis. The original version is the most standard.