Mønsteret og dekorasjonen er tydelige.

Because Norwegian usually puts the definite article on the end of the noun.

• mønster = pattern
• mønsteret = the pattern
• dekorasjon = decoration
• dekorasjonen = the decoration

So the sentence uses two definite singular nouns: the pattern and the decoration.

They are both singular.

Even though the whole subject is plural in meaning, each individual noun is singular:

• mønsteret = the pattern (singular)
• dekorasjonen = the decoration (singular)

They become a plural subject only because they are joined by og (and).

Because two singular nouns joined by og act together as a plural subject.

So:

• Mønsteret er tydelig. = The pattern is clear/distinct.
• Dekorasjonen er tydelig. = The decoration is clear/distinct.
• Mønsteret og dekorasjonen er tydelige. = The pattern and the decoration are clear/distinct.

The adjective agrees with the whole subject, not just with one noun.

In Norwegian, the present-tense verb does not change for singular and plural.

So er can mean both is and are, depending on the subject:

• Mønsteret er tydelig. = The pattern is clear.
• Mønsteret og dekorasjonen er tydelige. = The pattern and the decoration are clear.

This is simpler than English.

Not in this sentence.

Here, tydelige is used because the subject is plural.

That can be confusing because -e is also very common with adjectives in definite noun phrases, for example:

• det tydelige mønsteret = the clear/distinct pattern

But in your sentence, tydelige comes after er, so it is a predicate adjective, and the important reason for -e here is that the subject is plural.

Because it is a predicate adjective. It describes the subject through the verb er (is/are).

This works much like English:

• The pattern is clear.
• Mønsteret er tydelig.

If you wanted the adjective directly before the nouns, you would need a different structure, for example:

• det tydelige mønsteret og den tydelige dekorasjonen

That means something like the clear/distinct pattern and the clear/distinct decoration.

The dictionary forms are:

• et mønster = a pattern
  
  • definite singular: mønsteret
• en dekorasjon = a decoration
  
  • definite singular: dekorasjonen

So:

• mønster is neuter
• dekorasjon is common gender

That is why one gets -et and the other gets -en in the definite singular.

In standard Norwegian, yes — tydelige is the expected form here.

Because the subject is plural overall, the adjective should also be plural:

• correct: Mønsteret og dekorasjonen er tydelige.
• not standard here: Mønsteret og dekorasjonen er tydelig.

You could say:

• Et mønster og en dekorasjon er tydelige.

That means A pattern and a decoration are clear/distinct.

Notice that tydelige stays plural, because there are still two things joined by og.

Ø is a vowel English does not have exactly.

A rough comparison is the vowel in French deux or German schön. For an English speaker, it may sound a bit like a rounded version of the vowel in bird, but that is only approximate.

So mønsteret is roughly pronounced like MUHN-steh-ret, with the first vowel rounded.