Jeg går ind i stuen, når det begynder at regne.

Because Danish often uses the present tense for both:

• general/habitual actions: Whenever it starts raining, I go into the living room
• future actions: I’ll go into the living room when it starts raining

So Jeg går ... når det begynder ... is completely natural Danish. Context tells you whether it means a habit or a future event.

English does something similar in the when-clause: when it starts raining, not when it will start raining.

Literally, gå often means walk or go on foot. In this sentence, though, English usually just says go:

• Jeg går ind i stuen = I go into the living room

In a situation like moving from one room to another, English normally does not need to emphasize walking, even though Danish uses gå.

Because the two parts do different jobs:

• ind = in / inward / inside
• i = in / into before a noun

So:

• gå ind = go in
• gå ind i stuen = go into the living room

The combination ind i shows movement into something.

Because stuen means the living room, while en stue means a living room.

Danish usually adds the definite article to the end of the noun:

• en stue = a living room
• stuen = the living room

So i stuen means in/into the living room.

It can be understood as either, depending on context.

With når, Danish often expresses:

• a future time: when it starts raining
• a repeated/general situation: whenever it starts raining

So this sentence could mean:

• I go into the living room when it starts raining
• Whenever it starts raining, I go into the living room

Both are possible.

Because når is used for when/whenever, while hvis means if.

• når suggests something that happens at a certain time, or something that regularly happens
• hvis is more purely conditional: if

So:

• Jeg går ind i stuen, når det begynder at regne = I go into the living room when/whenever it starts raining
• Jeg går ind i stuen, hvis det begynder at regne = I go into the living room if it starts raining

The second version sounds more like a condition; the first sounds more like a normal response or expected event.

Because Danish, like English, often needs a subject even when there is no real person or thing doing the action.

Here det works like English it in weather expressions:

• det regner = it is raining / it rains
• det begynder at regne = it begins to rain

This det does not refer to a specific object. It is just a grammatical subject.

Because after at, Danish uses the infinitive form of the verb.

• infinitive: regne = to rain
• present tense: regner = rains / is raining

So:

• begynder at regne = begins to rain

You use regner only when the verb itself is finite, for example:

• Det regner = It is raining

Yes. A very common alternative is:

Når det begynder at regne, går jeg ind i stuen.

Notice the word order in the main clause:

• ... går jeg ...
• not ... jeg går ...

That happens because Danish main clauses normally follow the verb-second pattern. When the sentence starts with the når-clause, the finite verb går comes before the subject jeg in the main clause.

Because the sentence contains a main clause and a subordinate clause.

• main clause: Jeg går ind i stuen
• subordinate clause: når det begynder at regne

In Danish, some writers use start comma, which places a comma before a subordinate clause, as in your sentence.

So this version is normal:

Jeg går ind i stuen, når det begynder at regne.

You may also see Danish written without that comma, depending on the comma system being used.

Not if you want the same meaning.

There is an important difference:

• gå ind i stuen = go into the living room
  → movement from outside the room to inside it
• gå i stuen = walk in the living room / be walking around in the living room
  → movement inside the room, not entering it

So ind i is important here because it shows entering the room.