Jeg tager min frakke af, når jeg kommer ind i huset.

Because tage af is a fixed verb expression meaning to take off in the sense of removing clothing.

In Danish, some verbs combine with a small word like af, på, op, or ud, much like English phrasal verbs. In a main clause, that small word often gets separated from the verb:

• Jeg tager min frakke af. = I take off my coat.

If the verb is in the infinitive, the parts usually stay together:

• Jeg vil tage min frakke af.

So tager is the main verb, and af belongs with it.

Use min because the subject and the possessor are both jeg.

In Danish, sin/sit/sine is only used when the possessor refers back to a third-person subject such as han, hun, den, det, or de.

So:

• Jeg tager min frakke af. = I take off my coat.
• Han tager sin frakke af. = He takes off his own coat.

You cannot use sin with jeg.

Danish often uses the present tense for:

• habits
• general truths
• scheduled or expected future events

Here the sentence sounds like a regular habit or a normal sequence of events:

• Jeg tager min frakke af, når jeg kommer ind i huset.

So it means something like I take off my coat when I come into the house / whenever I come into the house.

This is very similar to English, which also often uses the present after when in this kind of sentence.

Når is used for something that happens:

• repeatedly
• generally
• in the future

Da is normally used for:

• one specific event in the past

So in this sentence, når is correct because it expresses a general rule or repeated action:

• Jeg tager min frakke af, når jeg kommer ind i huset.
  = I take off my coat when I come into the house / whenever I come into the house.

Compare:

• Da jeg kom ind i huset, tog jeg min frakke af.
  = When I came into the house, I took off my coat.

Because ind adds the idea of movement inward.

• komme i huset would sound unnatural here
• komme ind i huset means come into the house

The pattern is:

• komme ind i = come into
• gå ind i = go into
• løbe ind i = run into

So ind is important because it shows entering.

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

So:

• et hus = a house
• huset = the house

This is one of the big differences from English. Instead of a separate word like the, Danish often uses an ending:

• frakke = coat
• frakken = the coat
• hus = house
• huset = the house

In this sentence, i huset means in the house.

In Danish subordinate clauses, the subject usually comes before the verb in normal order:

• når jeg kommer ind i huset

That is different from main clauses, where Danish often has verb-second word order:

• Jeg tager min frakke af.
• Nu tager jeg min frakke af.

But after a conjunction like når, the subordinate clause keeps the more straightforward order:

• når + subject + verb

So når jeg kommer ind i huset is exactly what you should expect.

Yes. If the subordinate clause comes first, the main clause must still follow Danish verb-second word order.

So:

• Når jeg kommer ind i huset, tager jeg min frakke af.

Notice that after the initial clause, the verb tager comes before the subject jeg in the main clause.

That is a very common Danish pattern.

It is used for many items of clothing and also for things like glasses or shoes.

Examples:

• tage skoene af = take off the shoes
• tage jakken af = take off the jacket
• tage hatten af = take off the hat
• tage brillerne af = take off the glasses

So tage ... af is the normal expression for removing something from the body.

Sometimes yes, but it changes the wording a bit.

• når jeg kommer ind i huset = when I come into the house
• når jeg kommer indenfor = when I come inside

Both can work, but ind i huset is more specific because it literally mentions the house. Indenfor is more like inside/indoors.

So the original sentence is perfectly natural if you want to emphasize entering the house itself.

Because Danish does not need extra helping words in the same way English sometimes does.

English often uses auxiliary verbs like:

• do
• am/is/are
• will

Danish often expresses the idea more directly with the main verb:

• Jeg tager min frakke af = I take off my coat
• Jeg kommer ind i huset = I come into the house

So the Danish sentence can look shorter and more direct than the English one.

You would usually change both the tense and the conjunction:

• Jeg tog min frakke af, da jeg kom ind i huset.

Here:

• tog = took
• kom = came
• da = when, referring to a specific past event

That contrasts with the original present-tense, habitual sentence:

• Jeg tager min frakke af, når jeg kommer ind i huset.

So the original is more like a habit or regular pattern, while the past version describes one completed occasion.