O descanso vai melhorar a tua saúde.

In Portuguese, abstract nouns and general concepts often take a definite article, even when English would use no article.
So o descanso is literally the rest, but in context it just means rest in general.

Compare:

• O descanso é importante. – Rest is important.
• A saúde é tudo. – Health is everything.

You could technically say Descanso vai melhorar a tua saúde, but it sounds unnatural; the article is normally used here.

In this sentence descanso is a noun meaning rest.
The verb is descansar = to rest.

Both are possible but slightly different:

• O descanso vai melhorar a tua saúde. – Focus on rest (as a thing).
• Descansar vai melhorar a tua saúde. – Focus on the action of resting.

Both are correct and natural; the original sounds a bit more like a general statement or advice.

Portuguese has two common future forms:

1. Periphrastic future: ir + infinitive

   • vai melhorar – is going to improve / will improve
     This is much more common in everyday spoken European Portuguese.

2. Synthetic future: melhorará

   • Sounds more formal, written, or literary in modern usage.

So vai melhorar is the natural, conversational choice here.

tua corresponds to tu (informal singular you) in European Portuguese.
sua corresponds to você / ele / ela (your / his / her), and in European Portuguese it’s often more distant or formal, and also ambiguous (it can mean his, her, your, their).

So:

• Speaking informally to one person you know well: a tua saúde
• Speaking formally (e.g. to a patient) or about someone else: a sua saúde

Because the sentence clearly sounds like advice to someone you’re close to, tua is the best fit.

In European Portuguese, possessives are normally used with a definite article:

• a tua saúde
• o teu carro
• os teus amigos
• as tuas mãos

You can drop the article (tua saúde) in some contexts (poetic style, strong emphasis, some fixed expressions), but in normal everyday European Portuguese a tua saúde is more natural and more frequent.

In Brazilian Portuguese, dropping the article (tua saúde, minha casa) is much more common than in Portugal.

They agree in gender and number with the thing owned, not with the owner:

• Masculine singular: o teu livro – your book
• Feminine singular: a tua casa – your house
• Masculine plural: os teus amigos – your (male/mixed) friends
• Feminine plural: as tuas amigas – your (female) friends

In a tua saúde, saúde is feminine singular, so you use tua.

Yes. vossa is the possessive for vocês (plural you).

Use:

• a tua saúde – talking to one person informally.
• a vossa saúde – talking to several people (e.g. a group):
  
  • O descanso vai melhorar a vossa saúde. – Rest will improve your health (all of you).

Again, the possessive agrees with the noun:

• o vosso filho, a vossa casa, os vossos amigos, as vossas férias.

saúde is feminine, so it takes a and tua: a tua saúde.

There’s no perfect rule, but many abstract nouns ending in -de are feminine:

• a saúde, a liberdade, a felicidade, a cidade.

You mostly learn the gender together with the noun: think a saúde, not just saúde.

Yes, that’s correct, but the focus changes slightly:

• O descanso vai melhorar a tua saúde.
  Highlights rest as the cause; starts with rest as the topic.

• A tua saúde vai melhorar com o descanso.
  Highlights your health as the topic; then adds com o descanso (with rest) as the condition.

Both are natural; choose the one that matches what you want to emphasise first.

Yes, and it changes the nuance:

• O descanso vai melhorar a tua saúde.
  Rest in general; the idea of resting as a habit or state.

• Um descanso vai melhorar a tua saúde.
  More like a break / a period of rest; one instance of rest, not rest in general.

So um descanso is more specific, like a good break will do you good.

Approximate pronunciations (European Portuguese):

• descanso – /dɨʃˈkɐ̃su/

  • initial de-: very reduced, almost like a short, weak d
    • schwa sound;
  • -can-: nasal ã;
  • final -so: sounds like -su.

• tua – /ˈtu.ɐ/

  • tu- like English too;
  • final -a is a very short /ɐ/ sound.

• saúde – /sɐˈuðɨ/

  • sa-: reduced sɐ;
  • -ú-: stressed u (like oo in food);
  • final -de is usually a soft ðɨ (like th in this
    • a short final vowel).