Trots att det regnar tar hon tunnelbanan till intervjun, eftersom det går snabbare.

Because Swedish has the V2 rule in main clauses: the finite verb (here tar) must be in the second position.
When you start the sentence with a clause like Trots att det regnar (a subordinate clause functioning as a fronted element), that whole clause takes position 1, so the verb must come next, and the subject comes after it:

• Trots att det regnar (position 1) tar (position 2) hon (after the verb) tunnelbanan …

If you start directly with the subject, you get normal order:

• Hon tar tunnelbanan …

Trots att works like although / even though and introduces a subordinate clause.
It’s commonly analyzed as trots (literally despite) + att (a subordinator roughly like that), but you can treat trots att as one fixed unit meaning although.

Compare:

• Trots regnet … = Despite the rain … (noun phrase)
• Trots att det regnar … = Although it’s raining … (clause)

It doesn’t refer to anything concrete. Det here is a dummy subject (also called a formal/expletive subject), just like English it in it rains.
Weather verbs in Swedish typically require det:

• det regnar = it’s raining
• det snöar = it’s snowing

Inside both subordinate clauses, Swedish uses normal subordinate clause word order: subject before verb:

• att det regnar (det + regnar)
• eftersom det går (det + går)

The “different” word order you notice is actually in the main clause after the initial subordinate clause, because of the V2 inversion:

• Trots att … tar hon …

So: subordinate clauses have S–V, while the following main clause still must obey V2.

In this sentence tar is an idiomatic use meaning to take/use (a mode of transport):

• ta tunnelbanan = take the subway/metro
• ta bussen = take the bus
• ta tåget = take the train

So it’s very close to English take the subway.

Swedish often uses the definite form when talking about a standard, known option in a context—similar to English the subway (as a system/mode of transport).

• hon tar tunnelbanan = she takes the subway (the metro system)

If you said en tunnelbana, it would sound like “a subway (train)” as one instance/object, which is not what you normally mean here.

Intervjun is definite and suggests a specific, already-identified interview (e.g., the interview she has scheduled). Swedish commonly uses the definite when it’s a particular event both speaker and listener can identify.

If it’s not specific/new information, you’d use indefinite:

• till en intervju = to an interview (some interview, not previously specified)

Till is used for movement toward a destination (literal or event-like destination):

• gå till jobbet = go to work
• åka till Stockholm = go to Stockholm
• åka till intervjun = go to the interview

You can also see på intervju meaning “at an interview / (going) for an interview,” but till intervjun is very natural when you’re emphasizing getting there.

Eftersom means because/since and gives a reason:

• … eftersom det går snabbare = because it’s faster

För att usually expresses purpose (“in order to”), not a reason:

• Hon tar tunnelbanan för att komma fram i tid. = She takes the subway in order to arrive on time.

So in your sentence, eftersom is correct because it explains the reason.

Literally, det går snabbare is “it goes faster,” but idiomatically it means it’s faster / it works faster / it takes less time.
Swedish often uses gå in expressions about how something works or how long it takes:

• Hur går det? = How’s it going? / How is it going?
• Det går fort. = It goes fast / It’s quick.
• Det går snabbare med tunnelbanan. = It’s faster by subway.

Here, det is again a dummy subject meaning roughly “that option/that way.”

Snabbare is the comparative form: faster (implying faster than some alternative, like walking or taking the bus).

• snabb = fast (base form)
• snabbt = fast (adverb/neutral form)
• snabbare = faster

If you used snabbt, it would mean “it goes fast,” not explicitly “faster (than something else).”

Not strictly. Swedish comma rules are more flexible than English. Many writers omit the comma before a final eftersom-clause:

• … till intervjun eftersom det går snabbare.

A comma is often used to improve readability or signal a clearer pause, but it’s usually optional in sentences like this.