El solista empezó a entonar la balada del repertorio.

Because empezar is one of the verbs that normally takes a + infinitive when it means to begin/start doing something.

• empezó a entonar = started to intone / started singing
• empezó a hablar = started to speak
• empezó a llover = it started to rain

So in this structure, the a is required.

Empezó is the preterite form of empezar in the 3rd person singular: he/she/it started.

It is used because the sentence presents the action as a completed event in the past: the soloist started singing the ballad. If you used the imperfect, empezaba, it would sound more like was starting / used to start, which gives a different perspective.

Empezar is a stem-changing verb: e → ie in many present-tense forms:

• empiezo
• empiezas
• empieza

But in the preterite, that stem change does not happen for -ar and -er verbs like empezar. So you get:

• empecé
• empezaste
• empezó

That is why it is empezó, not empiezó.

The accent mark shows the stress and also distinguishes this form in writing.

• empezo would not be the correct standard spelling
• empezó is the correct preterite form: he/she started

In pronunciation, the stress falls on the last syllable: em-pe-ZÓ.

Here entonar means something like to intone, to strike up, or to begin singing in tune. In musical contexts, it can sound a bit more formal or literary than cantar.

So:

• cantar = the general verb to sing
• entonar = to intone / to begin singing / to sing with proper pitch

In this sentence, entonar gives a slightly more musical or elevated tone than plain cantar.

Del is the contraction of de + el:

• de el repertorio → del repertorio

This contraction is normally mandatory in Spanish when de is followed by the masculine singular article el.

So:

• la balada del repertorio = the ballad from the repertoire

One important exception: if El is part of a proper name, you do not contract it, for example de El Escorial.

Spanish uses definite articles more often than English does. In this sentence, each noun is presented as specific or identifiable in context:

• El solista = the soloist
• la balada = the ballad
• del repertorio = from the repertoire

Even where English might sometimes sound natural without an article, Spanish often still uses one.

Solista is a common-gender noun. The noun itself stays the same, but the article changes:

• el solista = the male soloist
• la solista = the female soloist

So if the soloist were female, the sentence would begin La solista empezó...

Repertorio means repertoire: the collection of pieces a singer, group, orchestra, or performer knows or performs.

So la balada del repertorio means the ballad from the repertoire or the ballad in the repertoire. Depending on context, in natural English it might also be understood as one of the songs in their set/list of pieces.

Yes. Comenzó a entonar is perfectly correct and means almost the same thing.

In many contexts, empezar and comenzar are interchangeable:

• empezó a entonar
• comenzó a entonar

Comenzar can sound slightly more formal or literary in some situations, but both are normal.

Yes: El solista empezó a cantar la balada del repertorio is grammatically correct.

The difference is mainly in nuance:

• cantar = neutral, everyday to sing
• entonar = more musical, formal, or stylistic

So entonar sounds a bit more polished or descriptive.

In standard Peninsular Spanish, the z in empezó is pronounced like the th in think.

So roughly:

• empezó ≈ em-pe-THO

Also, the stress is on the last syllable: -zó. This pronunciation is typical of most of Spain, though some regional accents differ.

Yes, Spanish word order is flexible, though the original order is the most neutral:

• El solista empezó a entonar la balada del repertorio.

You could change it for emphasis, for example:

• La balada del repertorio empezó a entonarla el solista.
  This is much less neutral and more marked.

For learners, the original SVO-style order is the best model to follow.