Su hermana también tiene mucha personalidad cuando habla en público.

In Spanish, su can mean several things depending on context:

• his
• her
• your (formal singular, like usted)
• their
• your (formal plural in some contexts)

So su hermana could mean his sister, her sister, your sister, or their sister.
You usually know which one is meant from the situation or previous conversation.

If Spanish speakers want to make it clearer, they can add:

• la hermana de él
• la hermana de ella
• la hermana de usted
• la hermana de ellos

In this sentence, su hermana most naturally means his/her sister unless the wider context says otherwise.

Yes, también means also / too, and its position can be somewhat flexible.

In your sentence:

• Su hermana también tiene mucha personalidad...

this means Her/His sister also has a lot of personality...

That placement is very natural because también is modifying the verb phrase tiene mucha personalidad.

Other placements are sometimes possible, but they may change the emphasis slightly. For example:

• También su hermana tiene mucha personalidad...
  This is possible, but less neutral and sounds more marked or literary.

The version in your sentence is the most standard and natural choice.

Not completely literal. Tener mucha personalidad is a common expression.

It usually means someone has:

• a strong presence
• a distinctive character
• confidence
• charisma
• a noticeable way of expressing themselves

So it does not mean they have many personalities.

Depending on context, mucha personalidad can be positive:

• confident
• expressive
• charismatic

But sometimes it can suggest someone is a bit strong-willed or dominant. In this sentence, it most likely sounds positive: she comes across strongly when speaking in public.

Mucha is the feminine singular form of mucho because personalidad is a feminine singular noun.

Agreement works like this:

• mucho for masculine singular
• mucha for feminine singular
• muchos for masculine plural
• muchas for feminine plural

Examples:

• mucho talento
• mucha personalidad
• muchos amigos
• muchas ideas

So mucha personalidad is correct because personalidad is feminine.

Spanish often leaves out subject pronouns when the verb ending already shows who the subject is.

Here, habla means he/she speaks, and from the context we understand the subject is su hermana.

So instead of saying:

• Su hermana también tiene mucha personalidad cuando ella habla en público

Spanish normally prefers:

• Su hermana también tiene mucha personalidad cuando habla en público

Using ella here is not wrong, but it usually sounds unnecessary unless you want extra emphasis or contrast.

The understood subject is su hermana.

So the sentence means that the sister has a lot of personality when she speaks in public.

In Spanish, once a subject has been mentioned, it is very common for later verbs to omit it if the meaning is still clear.

So this structure is interpreted as:

• Su hermana también tiene mucha personalidad cuando ella habla en público

but with ella left out because Spanish usually does not need it.

Because this sentence describes a usual or general situation.

• cuando habla en público = when she speaks in public / when she speaks publicly

The present indicative is used here because it refers to something habitual or generally true.

If you used cuando hable, that would usually point more to a future event:

• Cuando hable en público, tendrá que prepararse bien.
  When she speaks in public, she will have to prepare well.

So in your sentence, habla is correct because it describes a recurring trait or pattern.

En público means in public or before an audience, depending on context.

Here, because the sentence is about speaking, it is very close to:

• in public
• in front of people
• before an audience

It is a fixed expression, so Spanish says:

• hablar en público

not usually hablar en el público for this meaning.

So:

• Habla en público muy bien = She speaks well in public

Because en público is an established expression in Spanish.

Just as Spanish has fixed combinations like:

• a mano
• en serio
• de repente

it also has:

• en público

You usually learn it as a chunk meaning in public.

If you said en el público, that would usually mean something different, more like among the audience or in the crowd, not publicly.

Compare:

• Habla en público = She speaks in public
• Está en el público = She is in the audience

Not always in the exact same way.

Although personalidad often does mean personality, the expression tener mucha personalidad can sound more natural in English as:

• to have a strong personality
• to have a lot of presence
• to be very charismatic
• to have real character

So a very literal translation is possible, but sometimes English uses a slightly different phrase to sound natural.

Yes, it sounds completely natural in Spanish from Spain.

Everything in it is standard and common:

• su hermana
• también
• tener mucha personalidad
• cuando habla
• en público

A native speaker from Spain would easily say and understand this sentence. It sounds neutral and idiomatic.

Yes, but the nuance changes slightly.

• cuando habla en público = when she speaks in public
• al hablar en público = when speaking in public / while speaking in public

Cuando habla en público is more straightforward and probably the most natural here.

Al hablar en público sounds a bit more formal or descriptive, and it focuses more on the act itself.

So both can work, but your original sentence is the most neutral everyday option.