La que revisa el informe es mi jefa.

La que is an article + relative pronoun structure meaning the one who / she who / the person who. It introduces a relative clause (revisa el informe) and acts as the subject of the main verb es.
So the whole chunk La que revisa el informe = The one who checks/reviews the report.

Because it refers to a female person, and later the sentence specifies mi jefa (female boss).

• La que… = the (female) one who…
• El que… = the (male) one who…
• Lo que… usually means what (the thing that…), not a person: Lo que revisa… would sound like you’re talking about a thing, not a person.

You can often use quien for people, but the structure changes:

• Quien revisa el informe es mi jefa. = The person who reviews the report is my boss.
  That version is gender-neutral in the relative pronoun.
  La que is more specific because it marks feminine and is very common in Spanish.

La cual (and el cual / los cuales / las cuales) is a more formal/heavier relative option. Here, la que is the normal everyday choice.
You could say:

• La que revisa el informe es mi jefa. (natural)
• La cual revisa el informe es mi jefa. (more formal; can sound stiff in speech)

Yes. La que revisa el informe works like a noun phrase meaning the woman who reviews the report.
That entire phrase is the subject of es:

• Subject: La que revisa el informe
• Verb: es
• Complement: mi jefa

Because this is an identification statement: X is my boss. Spanish uses ser to identify or define what someone is.
Estar would imply a temporary state/location, which doesn’t fit:

• … es mi jefa = she is my boss (identity/role)
• … está would not work here unless you changed the meaning (e.g., location).

The Spanish present tense can cover both habitual and current actions depending on context:

• revisa can mean reviews/checks (as a role/habit) or is reviewing (right now).
  Without extra context, it’s often read as the one who (is in charge of) reviewing/checking the report.

In Spanish, que is the most common relative word and often covers who/that/which in English. The article (la) supplies gender/number information, and que introduces the relative clause:

• la que = the one who/that…

Yes, and it’s very common. The meaning is essentially the same, but the focus changes:

• La que revisa el informe es mi jefa. Focus on identifying who the reviewer is.
• Mi jefa es la que revisa el informe. Focus on your boss and what she does (or her responsibility).

In modern Spanish you normally don’t use an article with a possessive like mi:

• mi jefa (standard)
  Articles can appear in special cases (e.g., la casa de mi madre is fine, but that’s a different structure). For my + noun, you typically just use mi.

You’d change the gendered parts:

• El que revisa el informe es mi jefe.
  If you keep mi jefe (male boss), then El que matches it.

Often, but not only. el/la/los/las que can refer to people or things, depending on context.
For “what” (an idea/thing in general), Spanish typically uses lo que:

• Lo que revisas es importante. = What you’re reviewing is important.
  But for a specific female person, la que fits perfectly.