Mi hermano tiene un carácter tranquilo, pero se enoja cuando no respetan su espacio privado.

Both are possible, but they don’t sound exactly the same.

• Mi hermano es tranquilo focuses on your brother himself being a calm person in general.
• Mi hermano tiene un carácter tranquilo literally says “my brother has a calm temperament.” It highlights his nature or temperament as a trait.
• Using tiene un carácter… can sound a bit more formal, descriptive, or psychological, like you’re talking about personality as a characteristic rather than just giving a simple adjective.

No, it’s not the same as “a character in a story.”

• In this sentence, carácter means “temperament, disposition, personality type.”
• It’s closer to saying “He has a calm temperament / nature / disposition.”
• For “a character in a book/film,” Spanish usually uses personaje, not carácter.

Most adjectives in Spanish go after the noun.

• The normal order is noun + adjective: carácter tranquilo, casa grande, niño inteligente.
• Putting the adjective before the noun (tranquilo carácter) is either poetic, old-fashioned, or used for special stylistic effect. In everyday speech, carácter tranquilo is the natural form.

You normally use the indefinite article un here.

• Tiene un carácter tranquilo is the standard, natural way to say it.
• Saying tiene carácter tranquilo is grammatically possible, but it sounds incomplete or unusual in everyday speech.
• Compare: Tiene un coche rojo (“He has a red car”) — you’d also use un there. Same idea with un carácter.

Spanish gender is partly predictable, but not always obvious from the ending.

• Carácter is masculine by convention: el carácter, un carácter tranquilo.
• The adjective must agree with carácter, so it’s tranquilo (masculine), not tranquila.
• You just have to memorize the gender of nouns like this one: el carácter, el lápiz, el problema, etc.

Enojarse is a reflexive verb meaning “to get angry” / “to become angry.”

• Se enoja = “He gets angry” (he becomes angry).
• Without se, enojar usually means “to anger someone” (to make someone angry):
  
  • Eso enoja a mi hermano. = “That makes my brother angry.”
• In this sentence, your brother is the one who becomes angry, so you need the reflexive form: se enoja.

Both involve being angry, but they focus on different things.

• Se enoja = “He gets angry / He becomes angry” → the process / reaction.
• Está enojado = “He is angry” → the state of being angry at a given moment.
• In the sentence, the focus is on what happens when people don’t respect his space, so se enoja (he gets angry) is the natural choice.

In Spanish, the subject pronoun is often dropped because the verb ending shows the subject.

• Respetan is 3rd person plural (they): they respect.
• So no respetan su espacio privado = “(They) don’t respect his private space.”
• The “they” here is indefinite/unspecified (people in general, others around him), which is common in Spanish and understood from context.

You don’t use a with respetar when the object is a thing or concept.

• Respetar algo = to respect something.
  → Respetan las reglas, respetan su espacio privado.
• You do use a when the object is a person:
  → Respetan a mi hermano.
• Since espacio privado is not a person, you say respetan su espacio privado (no a).

Both are understandable, but there’s a nuance.

• Espacio privado = literally “private space.” It can refer to:
  • physical areas that are his (room, office, things),
  • or more abstract privacy/boundaries.
• Espacio personal = “personal space,” often used for:
  • the physical distance around a person,
  • their comfort zone in social interactions.
• In many everyday contexts, both can overlap, but espacio privado leans a bit more toward “privacy / private area.”

By default, in this sentence, su clearly refers to mi hermano.

• The last singular person mentioned is mi hermano, so su espacio privado is understood as “his private space.”
• In more complex sentences, su can be ambiguous, and you might clarify with de él / de ella:
  • su espacio privado → el espacio privado de él (“his private space”).
• Here, though, context makes it clear that su = his (your brother’s).

Yes, that word order is perfectly natural too.

• Both:
  • …pero se enoja cuando no respetan su espacio privado.
  • …pero cuando no respetan su espacio privado se enoja. are correct and common.
• Spanish allows some flexibility in the placement of phrases like cuando… (when-clauses) without changing the meaning.

Yes, there are differences in nuance and regional usage.

• In Latin America, enojarse is the standard verb for “to get angry.”
• Enfadarse is more common in Spain for “to get angry.”
• Molestarse often means “to get bothered / annoyed” and is sometimes milder than enojarse.
• In your sentence (Latin American Spanish), se enoja is the most natural, standard choice.

Yes, you can say that, and it’s very natural.

• Mi hermano es tranquilo = “My brother is calm.”
  It describes him simply as a calm person.
• Mi hermano tiene un carácter tranquilo adds a subtle focus on his temperament / nature as a trait.
• In everyday conversation, people very often say es tranquilo, so your alternative is totally fine and idiomatic.