Hoy quiero llevar una trenza antes de salir.

Because querer is a conjugated verb of desire, and the next verb stays in the infinitive.

So the pattern is:

• quiero + infinitive
• quieres + infinitive
• queremos + infinitive

Examples:

• Quiero salir = I want to go out
• Quiero comer = I want to eat
• Quiero llevar una trenza = I want to wear a braid

In this sentence, quiero is the only conjugated verb in the main clause, and llevar depends on it.

Spanish often leaves out subject pronouns when they are clear from the verb ending.

• quiero already means I want
• so yo quiero is usually unnecessary

Both are possible:

• Quiero llevar una trenza
• Yo quiero llevar una trenza

Adding yo can give extra emphasis, contrast, or clarity, but in a normal sentence it is often omitted.

Yes, llevar can mean to carry, but it also very commonly means to wear.

In Spanish, llevar is used for things you have on your body or as part of your appearance:

• Llevar gafas = to wear glasses
• Llevar sombrero = to wear a hat
• Llevar el pelo corto = to wear your hair short
• Llevar una trenza = to wear your hair in a braid

So here llevar refers to hairstyle, not carrying something in your hand.

Usually yes. Una trenza means one braid or one plait.

So this sentence suggests a hairstyle with a single braid.

If you wanted to say two braids, you would say:

• dos trenzas

In Spain, trenza is the normal word. In English, a British learner may think of plait, while an American learner may think of braid.

Because Spanish usually uses an article with countable singular nouns.

• una trenza = a braid
• un sombrero = a hat
• una falda = a skirt

Leaving out the article here would sound incomplete or unnatural.

Also, una does not necessarily emphasize one strongly here. It often just introduces the noun naturally.

Llevar una trenza is understandable and natural enough, especially if the focus is on the hairstyle you want to have.

That said, in everyday speech, a Spaniard might also say:

• Hoy quiero hacerme una trenza antes de salir = Today I want to do/make myself a braid before going out

The difference is:

• llevar una trenza focuses on wearing the hairstyle
• hacerme una trenza focuses on creating/doing the hairstyle

So your sentence works well, but hacerme una trenza may sound more specific if you mean doing your hair yourself before leaving.

Because antes is followed by de before an infinitive.

The pattern is:

• antes de + infinitive

Examples:

• antes de comer = before eating
• antes de dormir = before sleeping
• antes de salir = before going out / before leaving

So antes salir is not correct.

Because after antes de, when the subject is the same as in the main clause, Spanish uses the infinitive.

Here the implied subject is the same person throughout:

• Hoy quiero llevar una trenza
• antes de salir

In other words, I want to wear a braid before I go out.

If the subject changes, Spanish often uses a different structure:

• antes de que él salga = before he goes out

So:

• same subject → antes de + infinitive
• different subject → often antes de que + subjunctive

Yes. Spanish word order is flexible, especially with time expressions like hoy.

These are all possible:

• Hoy quiero llevar una trenza antes de salir
• Quiero llevar una trenza hoy antes de salir
• Antes de salir, hoy quiero llevar una trenza

The first one is the most neutral and natural if you want to start with today.

Putting hoy first gives it a slight emphasis, as if setting the time frame:

• Today, I want to wear a braid before going out.

Yes. Salir can mean several related things, including:

• to go out
• to leave
• to head out

So antes de salir can be understood according to context.

For example:

• if you are talking about leaving the house for the day, before leaving
• if you are talking about going out socially, before going out

The Spanish itself is normal in either case.

Not in exactly the same way.

• llevar focuses on having something on / wearing it
• ponerse focuses on putting something on

For clothes:

• Quiero ponerme un abrigo = I want to put on a coat
• Quiero llevar un abrigo = I want to wear a coat

With hairstyles, ponerse is less natural here. For hair, Spanish is more likely to use:

• llevar una trenza
• hacerse una trenza

So llevar is the better choice if the idea is the hairstyle you want to have.