Cuando mi hermana viva sola, será más independiente.

Because after cuando referring to a future event, Spanish uses the present subjunctive.

• Cuando mi hermana viva sola... = When my sister lives/is living on her own... in the future
• vive is the present indicative, which would not fit this future meaning

This is a very common pattern in Spanish:

• Cuando llegue, te llamo.
• Cuando tenga tiempo, lo haré.
• Cuando mi hermana viva sola, será más independiente.

Even though English uses a present form after when, Spanish switches to the subjunctive when the event has not happened yet.

Because the sentence is talking about what will happen later.

The structure is:

• Cuando mi hermana viva sola = a future situation
• será más independiente = the result in the future

So Spanish uses:

• subjunctive in the cuando-clause
• future in the main clause

In English, we say When my sister lives alone, she will be more independent. Spanish works similarly in meaning, but the grammar is different in the first clause.

Yes, but it means something different.

Cuando mi hermana vive sola, es más independiente means something like:

• When my sister lives alone, she is more independent
• Whenever my sister lives alone, she is more independent

This sounds like a general truth, habit, or repeated situation.

But Cuando mi hermana viva sola, será más independiente refers to a specific future time that has not happened yet.

So the difference is:

• cuando + indicative = habitual, factual, or known situation
• cuando + subjunctive = future, unknown, or not-yet-realised situation

Because the action is still in the future and uncertain from the speaker’s point of view.

Your sister does not live alone yet, so it is not a present fact. Spanish treats that as something pending or not yet realised, and that is why the subjunctive appears.

This also happens with other time expressions:

• En cuanto llegue, empezamos.
• Después de que termine, saldré.
• Hasta que vuelva, esperaré.

The key idea is: if the action is future and not yet completed, Spanish often uses the subjunctive.

Sola agrees with mi hermana, which is feminine singular.

The base adjective is:

• solo = alone (masculine singular)
• sola = alone (feminine singular)
• solos = alone (masculine plural / mixed plural)
• solas = alone (feminine plural)

So:

• mi hermano vive solo
• mi hermana vive sola

Here, sola means alone / on her own, not only.

Because Spanish usually omits subject pronouns when they are not needed.

The verb ending already tells you the subject:

• será = he/she/it will be

Since mi hermana has already been mentioned, adding ella is unnecessary.

You could say:

• Cuando mi hermana viva sola, ella será más independiente

But that sounds more emphatic, as if you are stressing she.

In normal Spanish, leaving out the pronoun is more natural.

Because independiente is being treated as a quality or characteristic, so Spanish uses ser.

• ser independiente = to be an independent person / to have independence as a trait

Estar is usually used for states or conditions, but independiente normally goes with ser in this kind of sentence.

So:

• Es muy independiente.
• Será más independiente cuando viva sola.

Using estar here would sound unusual in most contexts.

Because in Spanish, a possessive adjective like mi normally replaces the article.

So you say:

• mi hermana
• tu hermano
• nuestra casa

Not:

• la mi hermana ❌

That structure is not standard modern Spanish.

Más means more.

So más independiente means more independent.

The sentence is making a comparison between:

• your sister now, or in her current situation and
• your sister in the future, when she lives alone

Spanish forms most comparisons like this:

• más + adjective
• más alto = taller
• más fácil = easier
• más independiente = more independent

Yes. Spanish allows some flexibility.

You can also say:

• Será más independiente cuando mi hermana viva sola.

This means the same thing. The difference is mainly focus:

• Cuando mi hermana viva sola, será más independiente.
  Focuses first on the future condition/time.
• Será más independiente cuando mi hermana viva sola.
  Focuses first on the result.

Both are natural.

It is pronounced roughly BEE-ba in standard Spanish pronunciation, with the stress on the first syllable: VI-va.

Yes, it is the same verb form from vivir, but the meaning depends on context.

Here:

• viva = (that) she lives / subjunctive form of vivir

In expressions like:

• ¡Viva España!

it means something like Long live Spain!

So the form is the same, but the use is different.