Mi hermana habla en público mejor de lo que cree.

Because mi is the possessive adjective meaning my.

• mi hermana = my sister
• mí with an accent is a pronoun meaning me after a preposition:
  • para mí = for me
  • a mí = to me

So here, since it is directly describing hermana, you need mi without an accent.

Habla is the present indicative of hablar and is the normal form used for:

• general facts
• habits
• abilities
• things that are usually true

So Mi hermana habla en público mejor de lo que cree means something like My sister speaks in public better than she thinks or My sister is better at speaking in public than she thinks.

If you said está hablando, that would mean she is speaking right now, which is not the idea here.

Hablar en público is a very common expression meaning:

• to speak in public
• to speak before an audience
• to do public speaking

So it does not just mean speaking somewhere outside. It refers to speaking where other people are listening, often formally or nervously.

Examples:

• Me da miedo hablar en público. = I’m afraid of speaking in public.
• Habla muy bien en público. = She speaks very well in public.

Because en público is a fixed expression.

In Spanish, some expressions use a noun without an article when they function almost like an adverbial phrase. En público means in public / publicly.

Compare:

• en público = in public
• en privado = in private

You would not normally say en el público here, because that would suggest something different or sound unnatural in this context.

This is one of the most common questions.

After a comparative like mejor, Spanish often uses de lo que when what follows is a clause with a verb.

So:

• mejor de lo que cree = better than she thinks

Here is the structure:

• mejor = better
• de lo que = than what / than ... that
• cree = she thinks

A useful rule:

• Use que before a number or direct comparison of quantities:
  • más de tres = more than three
  • más que tú = more than you
• Use de lo que when the comparison is followed by an idea/clause:
  • Es más difícil de lo que parece. = It is harder than it seems.
  • Corre más de lo que pensaba. = He runs more than I thought.

In modern Spanish, you may also see mejor que cree in some contexts, but mejor de lo que cree is the standard and safest choice here.

Here lo que means something like what or that which.

In mejor de lo que cree, it is part of the comparative structure, so the whole phrase means:

• better than what she thinks
• more naturally in English: better than she thinks

Lo here is a neuter article, used for ideas, situations, or abstract things, not for masculine nouns.

Examples:

• No entiendo lo que dices. = I don’t understand what you’re saying.
• Es más fácil de lo que parece. = It’s easier than it seems.

In this sentence, cree means she thinks, and the subject is understood to be mi hermana.

Spanish often omits subject pronouns when the meaning is clear from context.

So:

• Mi hermana habla en público mejor de lo que cree. = My sister speaks in public better than she thinks.

Even though cree could theoretically be he/she/it thinks or you (formal) think, the context makes it clear that it refers to my sister.

If you wanted to be explicit, you could say:

• Mi hermana habla en público mejor de lo que ella cree.

But adding ella is usually unnecessary unless you want emphasis.

Because Spanish usually leaves out subject pronouns when they are not needed.

English needs she thinks, but Spanish often just says cree if the subject is obvious.

So both are possible:

• Mi hermana habla en público mejor de lo que cree.
• Mi hermana habla en público mejor de lo que ella cree.

The version without ella is more natural in normal speech unless you want contrast or emphasis.

Yes. Mi hermana habla mejor en público is also natural.

Both word orders work:

• habla en público mejor
• habla mejor en público

However, many speakers may find habla mejor en público slightly more natural, because mejor often comes closer to the verb it modifies.

That said, the original sentence is perfectly understandable and correct.

Here mejor is functioning as an adverb, because it modifies the verb habla.

• Habla mejor = She speaks better

It is not describing a noun, so it is not an adjective here.

Compare:

• Es una mejor opción. = Here mejor describes opción, so it is adjectival.
• Habla mejor. = Here mejor modifies habla, so it is adverbial.

They are similar, and in many contexts both can work, but they are not always exactly the same.

• creer often means to believe
• pensar often means to think

In this sentence, cree sounds very natural because the idea is about her own belief about her ability.

• Mi hermana habla en público mejor de lo que cree. = She is better than she believes/thinks.

You could also hear:

• Mi hermana habla en público mejor de lo que piensa.

That is possible, but cree fits especially well when talking about self-confidence or self-perception.

No. It is used with many comparatives.

Examples:

• más de lo que esperaba = more than I expected
• menos de lo que parece = less than it seems
• peor de lo que pensaba = worse than I thought
• mejor de lo que imaginaba = better than I imagined

So the pattern is very common:

• comparative expression + de lo que
  • verb

It is a very useful structure to learn as a whole.

Yes, very often that is the implication.

Mi hermana habla en público mejor de lo que cree suggests:

• she is actually good at public speaking
• but she does not realise it fully
• she underestimates herself

So grammatically it is a comparison, but pragmatically it often carries the idea that her opinion of her own ability is too low.