Learn Hardcore Norwegian: Jeg hviler i stuen når jeg er trøtt. - I rest in the living room when I am tired.

i generally means in/inside a space: i stuen = in the living room.
på is more like on/at a surface or a place viewed more like a point (på bordet = on the table, på jobb = at work).

For rooms, i is the normal choice: i stuen, i kjøkkenet, i soverommet.

What tense is hviler, and why is it used?

hviler is present tense of the verb å hvile (to rest). Norwegian commonly uses the present tense for general habits and repeated situations, just like English:

Jeg hviler ... når ... = I rest ... when ... (a general pattern)

If you meant a specific past event, you’d use past tense:

Jeg hvilte i stuen da jeg var trøtt.

Is å hvile the most natural verb here, or would Norwegians say something else?

å hvile is correct and natural, especially in slightly “neutral” or formal phrasing. In everyday speech, people also often use:

å slappe av = to relax
So you might also hear: Jeg slapper av i stuen når jeg er trøtt.

hvile can feel a bit more like resting (because you need rest), while slappe av is relaxing.

Why is the word order når jeg er trøtt and not når er jeg trøtt?

Because når introduces a subordinate clause, and subordinate clauses in Norwegian have normal subject–verb order:

når jeg er trøtt = when I am tired

The question order (er jeg ...?) is only for direct questions:

Når er jeg trøtt? = When am I tired?

Do I always need a comma before når?

In Norwegian, it’s standard to put a comma before a subordinate clause introduced by words like når, fordi, at, hvis, som:

Jeg hviler i stuen, når jeg er trøtt.

Many writers would also omit the comma in very short sentences in informal writing, but the safer “rule-following” choice is to include it.

Why is jeg repeated? Can it be omitted the second time?

You normally repeat the subject in the subordinate clause:

... når jeg er trøtt (you need jeg there)

You can’t usually drop it the way you might in some other languages. Norwegian generally requires an explicit subject.

What’s the difference between når and da in sentences like this?

A common guideline:

når = when(ever), whenever; repeated/general situations; also future
da = when (that one time in the past); specific past event

So your sentence with a general meaning naturally uses når. If you were telling a story about one specific occasion, you might use da:

Jeg hvilte i stuen da jeg var trøtt. (That time, I rested in the living room when I was tired.)

Could the sentence start with Når ... instead? What happens to the word order?

Yes. If the subordinate clause comes first, Norwegian uses V2 word order in the main clause, meaning the verb comes right after the first element. So you get inversion:

Når jeg er trøtt, hviler jeg i stuen.

Notice it becomes hviler jeg, not jeg hviler, because the first position is already taken by Når jeg er trøtt.

What does trøtt mean exactly, and is it different from sliten?

Both relate to tiredness, but often with a nuance:

trøtt = sleepy / tired (needing rest or sleep)
sliten = worn out / exhausted (often from effort or work)

So trøtt fits well if you mean you want to rest because you feel sleepy or low on energy.

How do you pronounce trøtt and the letter ø?

ø is a rounded vowel (lips rounded) that doesn’t exist in standard English. It’s somewhat like the vowel in bird for some speakers, but with rounded lips.
trøtt is typically pronounced roughly like trøtt with a short vowel and a clear tt (often a “sharper” t than English).

If you’re using a dictionary, look for IPA like /trœtː/ (varies by dialect), where œ indicates the ø-sound and tː shows a long/held t sound.