La periodista informa al público.

Yes. Periodista is a noun with the same form for both genders.

• la periodista = the female journalist
• el periodista = the male journalist

So the word periodista itself does not change; the article tells you the gender.

Informa is the third-person singular present indicative form of informar.

It matches la periodista because that subject is singular.

• yo informo = I inform
• tú informas = you inform
• él / ella informa = he / she informs

So La periodista informa means The journalist informs or, depending on context, The journalist is informing.

Because al is the contraction of a + el.

• a el becomes al
• so al público literally comes from a el público

Here, a is used because informar commonly takes a before the person or group being informed.

So:

• informar al público
• informar a la gente
• informar a los estudiantes

Literally, yes: al = to the.

But in natural English translation, you usually would not say informs to the public. English just says informs the public.

This is a good example of Spanish and English using different prepositions or structures with the same verb.

Because el público is a collective noun. It is grammatically singular, even though it refers to a group of people.

It works like:

• the public
• the audience

So al público means the public as one group, not one single person.

The accent mark shows where the stress goes: PÚ-bli-co.

It also helps distinguish it from other words spelled similarly. For example:

• público = public, audience
• publico = I publish

So the accent is important both for pronunciation and meaning.

Yes. That is perfectly normal.

The sentence is complete as it is: La periodista informa al público.

But Spanish also often adds the topic with de or sobre:

• La periodista informa al público sobre la noticia.
• La periodista informa al público de la situación.

So this sentence simply leaves that information unstated.

Yes, but it changes the meaning.

• La periodista = the journalist
  This usually refers to a specific journalist already known from the context.
• Una periodista = a journalist
  This introduces one journalist, not a specific previously identified one.

So both are correct, but they do not mean exactly the same thing.

Yes, but La periodista informa al público is the most neutral and standard order.

Spanish can change word order for emphasis, for example:

• Al público informa la periodista.

That sounds more marked or literary. For everyday use, the original order is the best one to learn first:

• subject + verb + object

Yes. Spanish often drops subject pronouns, but here the subject is a full noun phrase, not a pronoun.

You could say simply:

• Informa al público.

But then the subject would just be understood from context: he/she/it informs the public.

Including la periodista makes it explicit who is doing the action.