El documental empieza en cuarenta minutos.

Because the subject is el documental, which is third person singular: it starts.

• yo empiezo = I start
• tú empiezas = you start
• él/ella empieza = he/she/it starts
• ellos empiezan = they start

So El documental empieza means The documentary starts.

Documental is a masculine singular noun in Spanish, so it takes el.

• el documental
• el libro
• el programa

In this sentence, el means the.

Yes, when documental is used as the noun meaning documentary, it is normally masculine: el documental.

Even though many words ending in -al can be adjectives, here it is functioning as a noun.

Example:

• Vi el documental ayer. = I watched the documentary yesterday.

Spanish often uses the present tense to talk about a scheduled future event, just like English does.

• The documentary starts in forty minutes.
• El documental empieza en cuarenta minutos.

This is very natural in both languages when talking about timetables, plans, or scheduled events.

You could also use a future idea in other ways, but the present is the most natural here.

Here, en cuarenta minutos means in forty minutes, that is, forty minutes from now.

It tells you when the documentary starts, not how long it lasts.

So:

• Empieza en cuarenta minutos = It starts forty minutes from now.

They express different ideas:

• en cuarenta minutos = in forty minutes / forty minutes from now
• durante cuarenta minutos = for forty minutes (duration)

Compare:

• El documental empieza en cuarenta minutos. = It starts in forty minutes.
• El documental dura cuarenta minutos. = The documentary lasts forty minutes.

That difference is very important.

Yes. Dentro de cuarenta minutos also means in forty minutes and is very natural.

So both of these work:

• El documental empieza en cuarenta minutos.
• El documental empieza dentro de cuarenta minutos.

Dentro de can feel a little more explicit, but both are correct.

Because Spanish uses en to express in + amount of time.

• en cinco minutos
• en una hora
• en cuarenta minutos

The preposition a is used for other time expressions, especially clock times:

• Empieza a las ocho. = It starts at eight.
• Empieza en cuarenta minutos. = It starts in forty minutes.

So:

• a las ocho = at eight o’clock
• en cuarenta minutos = in forty minutes

Yes. Comienza and empieza both mean starts / begins.

• El documental empieza en cuarenta minutos.
• El documental comienza en cuarenta minutos.

Both are correct. Empezar is often felt to be a little more common in everyday speech, but comenzar is also very normal.

Yes. The infinitive is empezar, and it is a stem-changing verb: e → ie in many present-tense forms.

Examples:

• empiezo
• empiezas
• empieza
• empezamos
• empezáis
• empiezan

Notice that nosotros and vosotros do not change their stem:

• empezamos
• empezáis

Because 40 in Spanish is simply cuarenta. Number words have fixed forms, and 40 does not change for gender here.

Some useful numbers around it:

• treinta = 30
• cuarenta = 40
• cincuenta = 50

And:

• cuarenta minutos = forty minutes

Yes, but the original order is the most neutral.

Standard:

• El documental empieza en cuarenta minutos.

You might also hear:

• En cuarenta minutos empieza el documental.

That version puts more emphasis on the time expression. Both are correct.

In standard Peninsular Spanish, a common pronunciation would be roughly:

el dokumental em-pjee-tha en kwa-ren-ta mi-nu-tos

A few useful points for Spain:

• z in empieza is pronounced like the th in think
• c before e/i is also often pronounced that way in Spain
• j is not in this sentence, but in Spain it is a strong throaty sound

So empieza in Spain sounds closer to em-pye-tha than em-pye-sa.

No, not naturally. This sentence means it starts in forty minutes.

If you want to say it lasts forty minutes, Spanish would normally use durar:

• El documental dura cuarenta minutos.

So:

• empieza en cuarenta minutos = starts in forty minutes
• dura cuarenta minutos = lasts forty minutes

Yes. El documental va a empezar en cuarenta minutos is also correct.

That structure is the near future:

• va a empezar = is going to start

Compare:

• El documental empieza en cuarenta minutos.
• El documental va a empezar en cuarenta minutos.

Both are natural. The present tense version is especially common for scheduled events.