Stjernebildet er synlig nær Karlsvogna.

Because -et marks the definite form of the noun: the constellation.

• et stjernebilde = a constellation
• stjernebildet = the constellation

This is very common in Norwegian: the definite article is usually added to the end of the noun rather than written as a separate word.

Stjernebilde is a compound noun, which is extremely common in Norwegian.

It is made from:

• stjerne = star
• bilde = picture/image

So literally it is something like star-picture, which corresponds to constellation.

In the sentence, it becomes stjernebildet in the definite form.

That is simply how Norwegian expresses this idea:

• er = is
• synlig = visible

So er synlig = is visible

This works much like English:

• The constellation is visible
• Stjernebildet er synlig

Synlig is an adjective here, describing the constellation.

After the verb å være (to be), Norwegian often uses the adjective in its basic form when describing something.

So:

• Stjernebildet er synlig = The constellation is visible

Compare:

• En stjerne er synlig
• Stjernen er synlig

In this kind of sentence, the adjective often stays the same. Norwegian adjectives do change in some other contexts, but not every adjective changes in every position.

Nær means near or close to.

In this sentence:

• nær Karlsvogna = near the Big Dipper

It is a common preposition-like word used for location.

Examples:

• Huset ligger nær skogen = The house is near the forest
• Månen er nær horisonten = The moon is near the horizon

Karlsvogna is the Norwegian name of the asterism known in English as the Big Dipper.

The ending -a here is part of the standard name. In Norwegian, some feminine nouns and names appear with this kind of ending in the definite form.

So you should mostly treat Karlsvogna as a fixed proper name.

Because it is a proper name.

Names of specific star groups, places, people, and similar things are capitalized in Norwegian, just as in English.

So:

• Karlsvogna = a specific named object in the sky

No, this is a very normal Norwegian sentence pattern:

• Subject: Stjernebildet
• Verb: er
• Description: synlig
• Location: nær Karlsvogna

So it follows a straightforward pattern similar to English:

• The constellation
  • is
    • visible
      • near the Big Dipper

Yes, you could, but the meaning is slightly different.

• Stjernebildet er synlig nær Karlsvogna = The constellation is visible near the Big Dipper
• Stjernebildet er nær Karlsvogna = The constellation is near the Big Dipper

The original sentence emphasizes visibility, while the second one only states location.

No. The gender comes from the whole noun stjernebilde, not just the first part of the compound.

The base word bilde is a neuter noun:

• et bilde
• et stjernebilde

That is why the definite form is:

• stjernebildet

In compounds, the last element usually determines the grammatical gender.

It would be:

Et stjernebilde er synlig nær Karlsvogna.

That means A constellation is visible near the Big Dipper.

Compare:

• et stjernebilde = a constellation
• stjernebildet = the constellation

A rough English-friendly approximation would be:

KARLS-vog-na

A few helpful notes:

• r is typically pronounced more clearly than in many English accents
• vog sounds somewhat like vohg
• the final a is pronounced, not silent

If you are learning spoken Norwegian, it is best to hear it from native audio, because stress and vowel quality matter a lot.

Usually this version is the most natural:

Stjernebildet er synlig nær Karlsvogna.

You might move parts around for emphasis in some contexts, but for a learner, the safest neutral order is:

• subject
• verb
• adjective/complement
• place expression

So the original sentence is a good standard model.