Jeg går i seng tidligt, selv om jeg ikke er træt nok endnu.

Gå i seng is a fixed Danish expression meaning to go to bed.
Just like English says go to bed, Danish uses gå (go/walk) here.

It refers to the action of going to bed, not necessarily sleeping yet.
If you want to talk about actually sleeping, Danish uses sove.

In this expression, Danish normally says i seng without the definite article.

That is because gå i seng is an idiomatic phrase: it means go to bed in a general sense, not go into the specific bed.
If you were talking about a particular bed as a physical object, sengen could appear in other contexts, but not usually in this fixed expression.

Grammatically, it is present tense.

But in Danish, the present tense is often used for:

• habits: I go to bed early
• planned/near-future actions: I’m going to bed early

So the exact time sense depends on context. Danish often does not need a special future form here.

Selv om means even though or although.

It introduces a contrast:

• Jeg går i seng tidligt = one fact
• selv om jeg ikke er træt nok endnu = a contrasting fact

So the sentence says that the speaker is going to bed early despite not being tired enough yet.

Yes. Selv om and selvom are both used in modern Danish.

They mean the same thing here.
So you may see both:

• selv om
• selvom

The sentence would still mean the same thing.

Because selv om introduces a subordinate clause.

In Danish main clauses, the finite verb usually comes early:

• Jeg er ikke træt nok endnu.

But in subordinate clauses, words like ikke usually come before the finite verb:

• ... selv om jeg ikke er træt nok endnu.

So this is a normal Danish word-order pattern: subject + ikke + verb

Here nok means enough.

So:

• træt = tired
• træt nok = tired enough

This is a very common pattern in Danish:

• gammel nok = old enough
• stor nok = big enough
• god nok = good enough

Do not confuse this with another use of nok, where it can mean probably.
In træt nok, it clearly means enough.

Here endnu means yet.

In negative sentences, ikke ... endnu often corresponds to English not ... yet:

• jeg ikke er træt nok endnu = I’m not tired enough yet

It suggests that the speaker may become tired enough later.

Yes, Danish allows some flexibility with adverb placement.

This sentence has:

• Jeg går i seng tidligt

But you will also often hear:

• Jeg går tidligt i seng

Both are possible.
Jeg går tidligt i seng is often felt to be the more neutral everyday order, while Jeg går i seng tidligt is still perfectly understandable and natural.

It can be, but Danish comma rules allow variation depending on the comma system being used.

So you may see both:

• Jeg går i seng tidligt, selv om jeg ikke er træt nok endnu.
• Jeg går i seng tidligt selv om jeg ikke er træt nok endnu.

Both can be acceptable.
So if you notice Danish commas seeming inconsistent, that is normal.

Yes, you could say something like Jeg lægger mig tidligt, but it is not exactly the same in tone.

• gå i seng = the standard, neutral way to say go to bed
• lægge sig = lie down / go lie down, with a slightly more physical sense

So gå i seng is the most natural choice in this sentence.