Jeg har et lille rum, hvor jeg læser i ro og mag.

Because rum is a neuter noun in Danish, so it takes et, not en.

• en is used with common-gender nouns
• et is used with neuter nouns

So:

• et rum = a room

Since rum is neuter, the phrase must be et lille rum.

This is a very common question. Normally, adjectives before a neuter singular noun often get -t:

• et stort hus = a big house

But lille is irregular here. The form lille is used before singular nouns of both genders:

• en lille stol
• et lille rum

So even though rum is neuter, you still say et lille rum, not et lillet rum.

Here, hvor means where.

It refers back to rum:

• et lille rum, hvor jeg læser
  = a small room where I read

It introduces a relative clause that gives more information about the room.

Because this is a subordinate clause, not a main question.

In Danish:

• main clauses usually follow verb-second order
• subordinate clauses usually keep the subject before the verb

So:

• Jeg læser = I read
• hvor jeg læser = where I read

But in a direct question:

• Hvor læser jeg? = Where do I read?

That is why jeg comes before læser in the sentence.

Læser is the present tense of at læse, meaning to read.

So:

• jeg læser = I read / I am reading

In Danish, the present tense can often cover both the simple present and the present continuous, depending on context.

I ro og mag is a fixed expression meaning something like:

• in peace and quiet
• calmly
• at ease
• without hurry or disturbance

In this sentence, it suggests reading in a relaxed, undisturbed way.

You should learn it as a whole phrase, because its exact meaning is more idiomatic than literal.

• ro means calm, peace, or quiet
• mag is an older word related to ease, comfort, or having time to do something without stress

In modern Danish, mag is not used very often by itself in everyday speech, but it survives in set phrases such as:

• i ro og mag

So learners usually meet mag as part of this expression rather than as a separate common word.

Yes, possibly, but the meaning can shift a little.

• rum = room, space
• værelse = room, usually more like a room in a home, often a bedroom or private room

Rum is a broader word. It can sound slightly more general or descriptive.
Værelse is often more specific.

So the original sentence is perfectly natural, but værelse could also work if you mean a specific room in a house or apartment.

Because Danish spelling normally uses a comma before a subordinate clause.

Here, hvor jeg læser i ro og mag is a clause that describes et lille rum, so a comma is placed before it.

This is standard in written Danish and is something English speakers often notice because comma rules are different in English.

Yes, jeg har is the normal and natural way to say I have.

• jeg = I
• har = have

So:

• Jeg har et lille rum = I have a small room

This is completely straightforward Danish.

Sometimes Danish uses som in relative clauses, but in this sentence hvor is the natural choice because it refers to a place.

• et rum, hvor jeg læser = a room where I read

Using hvor makes the location relationship clear.
That is the form a learner should prefer here.

It is singular.

You can tell because of et:

• et rum = one room

The plural is:

• rum = rooms

So the singular and plural forms are often the same in spelling, but the article helps show the difference.

Then you would say:

• Jeg har det lille rum, hvor jeg læser i ro og mag.

But this sounds more unusual in many contexts, because the small room suggests a specific room already known in the conversation.

A more natural definite form might depend on context, for example if you are contrasting rooms in a house. The original et lille rum is the most neutral way to introduce the room for the first time.