A mi vecino le encanta escuchar guitarra y violín mientras cena en la terraza.

Because encantar works like gustar, not like English to love.

In this structure, the person who feels the emotion is treated as an indirect object:

• a mi vecino = to my neighbor
• le = to him / to my neighbor

The thing that is loved is the grammatical subject:

• escuchar guitarra y violín mientras cena en la terraza

So the sentence is structured more like: Listening to guitar and violin while he has dinner on the terrace delights my neighbor.

That is why Spanish uses a mi vecino le encanta.

Yes, they refer to the same person, but this is normal in Spanish. It is called clitic doubling.

• le is the indirect object pronoun
• a mi vecino clarifies or emphasizes who that le refers to

So:

• Le encanta escuchar guitarra y violín = He loves listening to guitar and violin
• A mi vecino le encanta escuchar guitarra y violín = same idea, but now my neighbor is explicitly named

In sentences with gustar / encantar, this doubling is extremely common, and leaving out le would sound wrong here.

Because the grammatical subject is not guitarra y violín here. The subject is the whole activity:

escuchar guitarra y violín mientras cena en la terraza

That whole activity functions as one idea, so the verb is singular:

• le encanta = he loves it / he loves doing that

Compare:

• A mi vecino le encanta escuchar guitarra y violín.
  The subject is escuchar... → singular
• A mi vecino le encantan la guitarra y el violín.
  Now the subject is la guitarra y el violín → plural

Yes. After verbs like gustar, encantar, odiar, preferir, Spanish often uses the infinitive to talk about an activity.

So:

• le encanta escuchar = he loves listening
• me gusta leer = I like reading
• nos encanta viajar = we love travelling

English often uses -ing in this kind of sentence, but Spanish usually uses the infinitive.

Because escuchar takes a direct object directly.

English says:

• listen to music
• listen to the violin

Spanish says:

• escuchar música
• escuchar el violín

So in your sentence:

• escuchar guitarra y violín

There is no equivalent of English to after escuchar.

This suggests a general, non-specific idea: guitar and violin music/sound in general, rather than particular instruments.

So:

• escuchar guitarra y violín can sound like to listen to guitar-and-violin music
• escuchar la guitarra y el violín sounds more specific, like listening to those instruments themselves or to a particular performance

A learner should know that many speakers would also naturally say: escuchar la guitarra y el violín or escuchar música de guitarra y violín

So the version without articles is understandable, but it has a more general or slightly elliptical feel.

Because escuchar usually implies active, intentional listening, while oír is more like hearing something.

• escuchar = to listen
• oír = to hear

So:

• Le encanta escuchar guitarra y violín = he enjoys listening to it
• Oye guitarra y violín would just mean he hears it

In this sentence, the idea is clearly intentional enjoyment, so escuchar fits better.

The understood subject of cena is mi vecino.

Spanish often leaves out subject pronouns when the verb ending already makes the subject clear. This is called subject omission or pro-drop.

So:

• mientras cena = while he has dinner / while he is having dinner

Spanish does not need to say mientras él cena unless the speaker wants extra emphasis or contrast.

Because cena is indicative, and here the action is presented as a real or habitual one.

• mientras cena = while he is having dinner / while he has dinner
• mientras cene would usually suggest a more hypothetical, future, or not-yet-real context

In this sentence, the speaker is simply describing what he likes doing during dinner, so the indicative is the natural choice.

In Spain, terraza usually refers to an outdoor space such as:

• a terrace
• a patio
• a balcony-like area
• sometimes even the outdoor seating area of a bar or café

In this sentence, en la terraza most likely means on the terrace / out on the terrace, meaning an outdoor area where the neighbor has dinner.

Yes. Vecino is masculine singular, so it normally refers to a male neighbor.

• mi vecino = my male neighbor
• mi vecina = my female neighbor
• mis vecinos = my neighbors

The possessive mi looks the same for masculine and feminine nouns, so the gender is shown by vecino / vecina, not by mi.