Learn Hardcore Russian: Её биография пока короткая, но она уже мечтает стать инженером или программистом. - Her biography is short so far, but she already dreams of becoming an engineer or a programmer.

The есть form of быть exists but is usually not used in neutral present‑tense statements like this. The meaning is is understood from context and word order.

What does пока mean here, and how is it different from пока не or пока что?

In this sentence, пока means for now / so far / at the moment:

Её биография пока короткая – Her biography is still short for now.

Some related uses:

пока не
- verb – until:
  - Подожди, пока не придёт мама. – Wait until Mom comes.
пока что – very close in meaning to this пока, often just a bit more informal/emphatic:
- Пока что её биография короткая.

So here пока is about the temporary state: it’s short now, but that may change later.

Why is короткая in that form, and not something like короткий?

Короткая is a nominative feminine singular adjective. It agrees with биография, which is:

feminine
singular
in the nominative case (it’s the subject complement)

Agreement:

биография (fem. nom. sg.) → короткая (fem. nom. sg.)

If the noun were masculine, you’d see короткий:

рассказ короткий – the story is short
But with feminine биография, it must be короткая.

Why do we say мечтает стать инженером and not мечтает быть инженером?

Both are possible, but they’re used differently:

мечтать стать кем‑то – to dream of becoming someone (focus on change in the future, achieving a new status).
- Она мечтает стать инженером. – She dreams of becoming an engineer.
мечтать быть кем‑то – to dream of being someone (focus more on the state itself, often a bit more abstract).
- Она мечтает быть свободной. – She dreams of being free.

In the context of a profession or future career, стать + instrumental is the most natural and standard choice.

Why are инженером and программистом in that -ом form? What case is that?

Инженером and программистом are in the instrumental case.

With the verb стать (to become), Russian uses the instrumental case for the new role or profession:

стать инженером – to become an engineer
стать программистом – to become a programmer

So the pattern is:

стать
- стать учителем
  - стать врачом
  - стать актрисой (feminine instrumental, different ending)

Why is there no Russian word like a or an before инженером or программистом?

Russian does not have articles like a / an / the at all.

Where English needs:

an engineer, a programmer

Russian just uses:

инженер, программист (or, in this sentence, their instrumental forms инженером, программистом)

The idea of a / an is understood from context, without any extra word.

What’s the difference between мечтать о том, чтобы стать инженером and мечтать стать инженером?

Both mean to dream of becoming an engineer, but:

мечтать стать инженером is more direct and common in modern speech, especially with professions.
мечтать о том, чтобы стать инженером is longer, slightly more formal or stylistic, and can sound more emphatic or literary.

Meaning-wise, they are almost the same; the shorter form is typically preferred in everyday language.

What does уже add to она уже мечтает? Could we leave it out?

Уже means already. It emphasizes that she has started dreaming of this earlier than one might expect or sooner than some reference point.

Она мечтает стать инженером. – She dreams of becoming an engineer.
Она уже мечтает стать инженером. – She already dreams of becoming an engineer (maybe she’s still very young, but already has such ambitions).

You can grammatically leave уже out; the sentence remains correct. You’d just lose that nuance of already / by now.

What is the function of но here, and why is there a comma before it?

Но is the conjunction but, introducing contrast:

Её биография пока короткая, но она уже мечтает...
→ Her biography is still short, but she already dreams...

In Russian, a comma is normally required before coordinating conjunctions like но, и, а when they join two clauses:

Её биография пока короткая – first clause
она уже мечтает стать инженером или программистом – second clause

These two clauses are joined by но, so Russian spelling rules require a comma before но.

Why is it она after но, and not её биография again? Could it be ambiguous?

The pronoun она refers to the girl/woman, not to биография.

Contextually:

Её биография пока короткая – talks about the biography.
она уже мечтает... – now we are talking about the person whose biography this is, so we switch to она (she).

Native speakers understand that она is the person, because:

A биография cannot мечтать (dream); only a person can.
In the larger context (e.g., a text about a girl), она naturally refers back to that person.

Repeating её биография would sound clumsy and wrong here, because the subject of мечтать logically has to be the person.

Why is биография feminine, and how do I recognize its gender?

Most Russian nouns ending in -а / -я in the nominative singular are feminine.

Биография ends in -я, so:

биография – feminine noun
therefore, adjectives and pronouns referring to it must be feminine:
- её биография – her biography
- короткая биография – a short biography

This is a general rule:

комната, книга, неделя, история, Россия → all feminine because of -а / -я endings (with a few exceptions you meet later).

Is there any difference in meaning between короткая биография and something like маленькая биография?

Yes:

короткая биография – short in length (few facts, not much text). This is the normal, correct choice here.
маленькая биография – literally small biography; this sounds odd or metaphorical in Russian. You normally don’t call a biography маленькая unless you’re speaking very figuratively (e.g. physically small book, and even then короткая is better).

For texts, stories, lives, etc., to express short in length/duration, короткий / короткая is the usual adjective.

Why is или used and not something like и? Does или mean or in the same way as in English?

Или is the normal word for or:

инженером или программистом – an engineer or a programmer.

Using и would change the meaning:

инженером и программистом – an engineer and a programmer (both roles).

As in English, или can be:

exclusive or (one or the other), depending on context
inclusive or (one or both), in some contexts

Here it’s more naturally understood like English or in career choices: she hasn’t decided yet which of the two professions she wants.