La amante volvió ayer.

Because amante is a common-gender noun in Spanish. That means the noun itself does not change form for masculine and feminine; the article tells you the gender:

• el amante = the male lover
• la amante = the female lover

So in this sentence, la shows that the person is female.

Yes. Unlike pairs such as amigo / amiga, amante usually keeps the same form for both sexes:

• el amante
• la amante

This is common with many nouns ending in -ante, -ente, or -ista.

Spanish often leaves out subject pronouns when they are not needed. English normally says she returned yesterday, but Spanish can simply say:

• volvió ayer

The verb form volvió already tells you it is third person singular: he/she/it returned. Since la amante is already there, adding ella would usually be unnecessary.

Volvió is the preterite form of volver. It is third person singular in the pretérito indefinido:

• yo volví
• tú volviste
• él/ella volvió
• nosotros volvimos
• vosotros volvisteis
• ellos/ellas volvieron

In this sentence, volvió means returned / came back as a completed action in the past.

The accent mark shows the correct stress: vol-VIÓ.

Without the accent, volvio would not follow normal Spanish stress rules and would be incorrect. In preterite forms like this, the accent is a standard part of the spelling:

• volvió
• comió
• salió

So the accent is not optional; it is part of the correct written form.

Those are different tenses:

• vuelve = returns / is returning
• volvía = was returning / used to return
• volvió = returned

Because the sentence refers to a completed action yesterday, volvió is the natural choice.

Good question. Volver is a stem-changing verb in some tenses, but not in the preterite.

Compare:

• Present: vuelvo, vuelves, vuelve
• Preterite: volví, volviste, volvió

So the o → ue change happens in the present tense, but not here.

That is a very normal word order in Spanish. Ayer is an adverb of time, and Spanish often places time expressions at the end:

• La amante volvió ayer.

But Spanish word order is fairly flexible, so you could also hear:

• Ayer volvió la amante.
• La amante ayer volvió.
  This is possible, though less neutral.

The version with ayer at the end sounds straightforward and natural.

Yes:

• Ayer volvió la amante.

This puts a little more focus on when it happened. The original sentence, La amante volvió ayer, is more neutral and starts with the subject.

Both are grammatical.

Because ayer refers to a finished time period: yesterday is over. In Spanish, completed actions in a finished past time usually take the preterite:

• Ayer volvió.
• Ayer llegó.
• Ayer comió.

This is especially important in Spain, where learners often compare volvió and ha vuelto. With ayer, volvió is the standard choice.

Normally, no. In standard Spanish, especially in Spain, ayer usually goes with the preterite, not the present perfect:

• Correct: La amante volvió ayer.
• Usually not correct: La amante ha vuelto ayer.

The present perfect in Spain is more often used for actions connected to a time period that is still considered current, such as hoy in many regions:

• Hoy ha vuelto.

But with ayer, the usual form is volvió.

Yes. The article la means the, so it refers to a specific female lover already known from the context, or at least treated as identifiable.

If you wanted a female lover, you would say:

• Una amante volvió ayer.

So:

• la amante = the female lover
• una amante = a female lover