Selvom jeg er træt, vil jeg gerne skrælle en appelsin og smøre en skive rugbrød, før jeg går i seng.

Because Danish main clauses follow the V2 rule: the finite verb normally comes in the second position.

Here, the whole opening clause Selvom jeg er træt counts as the first element. That means the main-clause verb vil has to come next, and the subject jeg comes after it:

• Selvom jeg er træt, vil jeg gerne ...

If there were no opening clause, you would say:

• Jeg vil gerne ...

So this is not random inversion; it is standard Danish word order.

Because selvom and før introduce subordinate clauses.

In Danish subordinate clauses, the subject normally comes before the finite verb:

• selvom jeg er træt
• før jeg går i seng

So you do not say:

• selvom er jeg træt
• før går jeg i seng

A useful contrast is:

• Main clause: Vil jeg gerne ... / Jeg går ...
• Subordinate clause: ... jeg er ... / ... jeg går ...

Gerne often means something like gladly or with pleasure, but after vil it very often gives the meaning would like to.

So:

• Jeg vil skrælle en appelsin can sound like I want to / I intend to peel an orange
• Jeg vil gerne skrælle en appelsin sounds softer and more natural in many situations: I’d like to peel an orange

For learners, vil gerne is often the safest way to express a polite or ordinary wish.

Because vil is followed by the bare infinitive in Danish.

So you say:

• vil skrælle
• vil smøre

not:

• vil at skrælle
• vil at smøre

This is the same pattern you get with other common verbs of this type, such as:

• kan
• skal
• må

For example:

• Jeg kan svømme
• Jeg skal gå
• Jeg må vente

Because the two infinitives are joined by og and share the same subject and modal verb.

The structure is basically:

• vil jeg gerne [skrælle en appelsin] og [smøre en skive rugbrød]

This is completely normal. Danish, like English, does not repeat the modal unless there is a special reason to emphasize it.

Compare English:

• I would like to peel an orange and butter a slice of rye bread

You would not normally repeat would like to before the second verb either.

Because appelsin is a countable noun, while rugbrød is usually treated as a substance or mass noun in this kind of phrase.

• en appelsin = one orange
• en skive rugbrød = one slice of rye bread

Also, both appelsin and skive are en-words, so they take en in the indefinite singular.

In en skive rugbrød, the word being counted is skive. The word rugbrød just tells you what kind of slice it is.

Because Danish often puts a measure word directly before the noun without af.

So:

• en skive rugbrød
• et glas vand
• en kop kaffe

This works much like English:

• a slice of rye bread
• a glass of water
• a cup of coffee

English uses of here, but Danish often leaves that out.

Smøre literally means to spread or to butter.

With bread, it often means to put butter or some other spread on it, and by extension to prepare a piece of bread to eat. So smøre en skive rugbrød suggests something like:

• butter a slice of rye bread
• spread something on a slice of rye bread
• prepare a slice of rye bread

If you want to be more specific, Danish can also name what is being spread.

Because Danish often uses the present tense in time clauses when talking about the future.

So før jeg går i seng is the normal way to say:

• before I go to bed

This is actually similar to English. English also prefers:

• before I go to bed

rather than:

• before I will go to bed

So the Danish tense choice here is very natural.

Because gå i seng is a fixed expression meaning go to bed.

Here, seng is used in a more general, idiomatic way, not as a specific physical bed being identified. That is why you usually get:

• gå i seng = go to bed

By contrast, i sengen is more concrete and often refers to being in the bed itself:

• Jeg ligger i sengen = I am lying in the bed / in bed

So:

• gå i seng = the act of going to bed
• være i sengen = being in the bed

The comma after træt is there because the opening subordinate clause ends there:

• Selvom jeg er træt, vil jeg gerne ...

That comma is required.

The comma before før is more a matter of comma style. Many Danes still write it:

• ..., før jeg går i seng

But in modern Danish comma usage, it is also very common to leave it out:

• ... rugbrød før jeg går i seng

So the first comma is essential here; the second one depends more on the comma system or style being used.