Ей не хватает уверенности говорить перед публикой.

Because Russian uses the pattern кому-то не хватает чего-то for someone lacks something.

• ей is the dative form of она
• the person who experiences the lack goes in the dative
• the thing that is lacking goes in the genitive

So Ей не хватает уверенности literally means something like To her, there is not enough confidence.

Because не хватает requires the thing that is lacking to be in the genitive case.

So:

• уверенность = nominative
• уверенности = genitive singular

This is the same pattern as:

• Мне не хватает времени = I don’t have enough time
• Ему не хватает опыта = He lacks experience
• Им не хватает сил = They lack strength

So уверенности is exactly what you expect after не хватает.

It comes from the verb хватать. In this construction, не хватает means:

• is not enough
• is lacking
• to lack

So Ей не хватает уверенности can be understood literally as She does not have enough confidence or She lacks confidence.

A useful pair:

• Ей хватает уверенности = She has enough confidence
• Ей не хватает уверенности = She does not have enough confidence

The infinitive говорить explains what she lacks confidence for.

So the structure is basically:

• уверенности говорить = confidence to speak

Russian often does this with abstract nouns:

• смелости сказать = courage to say
• желания учиться = desire to study
• возможности поехать = opportunity to go

Here, говорить перед публикой tells you the action connected with the missing confidence.

The sentence is understandable, but many native speakers would find this version a bit more natural:

• Ей не хватает уверенности, чтобы говорить перед публикой.

That version makes the relationship clearer: she lacks enough confidence in order to speak before an audience.

So:

• уверенности говорить = compact, possible
• уверенности, чтобы говорить = more explicit and often smoother

Also note:

• without чтобы, there is no comma
• with чтобы, you normally do use a comma

Because говорить is imperfective and refers to speaking as a general activity.

Here the idea is not:

• saying one specific thing once

but rather:

• being able to speak in front of people in general

Compare:

• говорить перед публикой = to speak before an audience, as an activity
• сказать перед публикой = to say something before an audience, possibly one specific remark

So говорить fits better for general public speaking.

Often, yes.

If you mean public speaking, giving a talk, appearing before an audience, then выступать перед публикой is very natural.

So a very idiomatic version would be:

• Ей не хватает уверенности, чтобы выступать перед публикой.
• Ей не хватает уверенности в себе, чтобы выступать перед публикой.

By contrast:

• говорить = speak
• выступать = speak/perform/present before an audience

So говорить is not wrong, but выступать may match the situation better.

The preposition перед means before or in front of, and it takes the instrumental case.

So:

• публика = nominative
• публикой = instrumental

That is why the phrase is:

• перед публикой = before an audience / in front of an audience

This is a very common pattern:

• перед домом = in front of the house
• перед учителем = before the teacher
• перед публикой = before an audience

Here публика means something like:

• audience
• crowd
• spectators
• the people watching/listening

It does not always match every meaning of English the public.

In this sentence, перед публикой is best understood as before an audience.

A related word is аудитория:

• перед аудиторией = before an audience

That can sound a bit more neutral or formal.

This is a very useful distinction.

• перед публикой = before an audience, facing listeners/watchers
• на публике = in public, where other people can see you

So:

• говорить перед публикой = speak to an audience
• плакать на публике = cry in public

For stage speaking, presenting, or addressing listeners, перед публикой is the better choice.

Both are possible, but уверенности в себе is often clearer and more natural if you specifically mean self-confidence.

Compare:

• уверенности = confidence, certainty; the exact meaning depends on context
• уверенности в себе = self-confidence

So many speakers would prefer:

• Ей не хватает уверенности в себе, чтобы говорить перед публикой.

The original sentence is understandable, but в себе makes the meaning more explicit.

Yes, Russian word order is flexible, but the original order is the most neutral and easiest for learners:

• Ей не хватает уверенности говорить перед публикой.

If you move things around, you change the emphasis, and the sentence may sound more marked or less natural.

For example:

• Перед публикой ей не хватает уверенности говорить sounds much less natural

So while Russian allows movement for emphasis, it is best to keep the original order unless you have a specific reason to highlight one part.