Selv om jeg er vågen nu, går jeg tidligt i seng, hvis jeg skal op før klokken seks.

Here Selv om means although or even though. It introduces a contrast:

Selv om jeg er vågen nu = Although I’m awake now

You will also often see selvom written as one word in Danish. In practice, learners should recognize both when reading.

This is a very common Danish word-order pattern.

Danish main clauses usually follow the V2 rule, which means the finite verb comes in the second position. In this sentence, the first position is taken by the opening clause:

Selv om jeg er vågen nu

So in the main clause, the verb must come next:

går jeg tidligt i seng

If the main clause stood alone, it would be:

Jeg går tidligt i seng

But after an opening element like this, Danish switches to:

... går jeg ...

The commas mark subordinate clauses.

• Selv om jeg er vågen nu, is a subordinate clause before the main clause.
• hvis jeg skal op før klokken seks is another subordinate clause.

So the commas help show the structure:

• subordinate clause
• main clause
• subordinate clause

A useful extra note: Danish has two accepted comma styles. The sentence you were given uses start comma, where you also put a comma before a subordinate clause such as hvis.

Vågen is an adjective meaning awake.

So:

jeg er vågen = I am awake

After er, Danish often uses an adjective to describe a state:

• jeg er træt = I am tired
• jeg er glad = I am happy
• jeg er vågen = I am awake

So vågen is not a verb here; it is describing how the speaker is.

Because tidligt is being used as an adverb, not an adjective.

• tidlig = early (adjective)
• tidligt = early / early on (adverb)

In this sentence, it modifies the action går:

går tidligt i seng = goes to bed early

Compare:

• en tidlig morgen = an early morning
• jeg står tidligt op = I get up early

A lot of Danish adverbs are formed by adding -t to the adjective.

Gå i seng is the normal Danish expression for go to bed.

Literally, it is something like go into bed, but idiomatically you should just learn it as the fixed expression go to bed.

So:

jeg går tidligt i seng = I go to bed early

It is different from sove (to sleep). You can gå i seng without actually falling asleep right away.

Skal op is a very common expression meaning have to get up or sometimes need to be up.

So:

hvis jeg skal op før klokken seks = if I have to get up before six o’clock

The word op literally means up, and together with skal it gives the idea of getting up from bed, especially when talking about mornings:

• Jeg skal op klokken fem = I have to get up at five
• Jeg skal tidligt op i morgen = I have to get up early tomorrow

Hvis means if, so it introduces a condition.

That fits this sentence:

... hvis jeg skal op før klokken seks = ... if I have to get up before six

If you used når, the meaning would shift more toward when / whenever, something expected or repeated:

Når jeg skal op før klokken seks, går jeg tidligt i seng
= Whenever I have to get up before six, I go to bed early

So:

• hvis = if
• når = when / whenever

Danish often uses the present tense for:

• general habits
• regular behavior
• near-future situations

That is what happens here:

går jeg tidligt i seng
skal op

The sentence expresses a general rule about the speaker’s behavior, not only what is happening at this exact second.

English does something similar:

I go to bed early if I have to get up before six.

So the Danish present tense sounds completely natural here.

Før klokken seks means before six o’clock.

• før = before
• klokken seks = six o’clock

In Danish, klokken is very common in time expressions:

• klokken seks = six o’clock
• før klokken seks = before six o’clock
• efter klokken otte = after eight o’clock

In casual speech, people may sometimes shorten it, but klokken is very normal and standard.

Yes, it sounds natural. It combines several very common Danish patterns:

• Selv om ... for contrast
• går jeg ... because of Danish V2 word order
• gå i seng as the normal phrase for go to bed
• hvis jeg skal op ... as a natural way to talk about having to get up early

So it is a very useful sentence for learning both vocabulary and Danish sentence structure.