Merverdiavgiftsregisteret er offentlig.

Because Norwegian usually writes compound nouns as one word.

So where English often writes value added tax register, Norwegian packs the parts together:

• merverdiavgift = VAT
• register = register / registry

That gives merverdiavgiftsregister.

This is very normal in Norwegian. Long compound nouns can look intimidating, but they are usually just smaller words joined together.

A useful breakdown is:

• merverdi = added value
• avgift = tax / fee
• merverdiavgift = value-added tax
• register = register
• -et = the definite ending

So:

• merverdiavgiftsregister = VAT register
• merverdiavgiftsregisteret = the VAT register

That -s- is a linking sound/letter often used inside Norwegian compounds.

So:

• merverdiavgift
• register

becomes:

• merverdiavgiftsregister

This -s- is not the same as the English possessive 's. It is just a common way of joining parts of a compound noun in Norwegian.

Because register is a neuter noun.

Its forms are:

• et register = a register
• registeret = the register

In compounds, the last part usually decides the gender and inflection. Since the head word is register, the whole compound is also neuter:

• et merverdiavgiftsregister
• merverdiavgiftsregisteret

It is built into the noun itself.

In Norwegian, definite nouns usually take a suffix instead of a separate word:

• et register = a register
• registeret = the register

So Merverdiavgiftsregisteret already means the VAT register.

That is why there is no separate word before it for the.

Er is the present tense of å være = to be.

So:

• er = is / are

In this sentence, it works exactly like English is:

• Merverdiavgiftsregisteret er offentlig.
• The VAT register is public.

Because adjectives ending in -ig, -lig, and some similar endings often do not add an extra -t in the neuter singular.

So you get:

• et offentlig register
• registeret er offentlig

not normally:

• offentligt

This is a very common pattern in Norwegian. Compare:

• et viktig spørsmål = an important question
• spørsmålet er viktig = the question is important

Here viktig also stays the same.

Yes.

In your sentence, offentlig is used predicatively — after er:

• Merverdiavgiftsregisteret er offentlig.

But it can also be used before a noun:

• et offentlig merverdiavgiftsregister = a public VAT register

If the noun is definite and has an adjective before it, Norwegian normally uses double definiteness:

• det offentlige merverdiavgiftsregisteret

That structure is very common in Bokmål.

This sentence has the basic Norwegian statement pattern:

• subject + verb + complement

So:

• Merverdiavgiftsregisteret = subject
• er = verb
• offentlig = complement

It is also a good example of the Norwegian verb-second rule: in main clauses, the finite verb usually comes in the second position.

Here the subject comes first, so er comes second.

The indefinite form is:

• et merverdiavgiftsregister = a VAT register

Then the definite form is:

• merverdiavgiftsregisteret = the VAT register

So the sentence could be changed like this:

• Et merverdiavgiftsregister er offentlig.
  Grammatically possible, but now it means a VAT register is public, which is a more general statement.

Normally, no.

Norwegian does not capitalize common nouns the way German does. So in the middle of a sentence, you would usually write:

• merverdiavgiftsregisteret er offentlig

It has a capital M in your example because it is the first word of the sentence.