Mobilabonnementet er nyt.

Because Danish normally writes compound nouns as a single word.

So:

• mobil = mobile / cell phone
• abonnement = subscription / plan
• mobilabonnement = mobile subscription / mobile plan

Then -et is added to make it definite.

A useful rule: in Danish compounds, the last part is the main noun, and it decides the gender and inflection. Here the main noun is abonnement.

-et is the definite article ending for a singular neuter noun.

Compare:

• et mobilabonnement = a mobile subscription
• mobilabonnementet = the mobile subscription

So instead of putting a separate word like the before the noun, Danish often adds the definite ending directly to the noun.

Because the adjective has to agree with the noun’s gender and number.

The adjective ny changes like this:

• ny = singular common gender
• nyt = singular neuter
• nye = plural, and also often used before definite nouns

Since mobilabonnementet is singular and neuter, the correct form is nyt.

The gender comes from the main noun at the end of the compound: abonnement.

You say:

• et abonnement not
• en abonnement

So abonnement is neuter, and therefore mobilabonnement is also neuter:

• et mobilabonnement
• mobilabonnementet
• Mobilabonnementet er nyt

Because Danish usually expresses definiteness by adding it to the noun itself.

So:

• et mobilabonnement = a mobile subscription
• mobilabonnementet = the mobile subscription

English uses a separate article, but Danish often uses a suffix instead.

However, if you put an adjective before a definite noun, Danish usually uses a separate article:

• det nye mobilabonnement = the new mobile subscription

Notice that in this case it is det nye mobilabonnement, not det nye mobilabonnementet.

Because nyt here is a predicative adjective: it comes after er and describes the subject.

In Danish, predicative adjectives usually agree with:

• gender
• number

but not with definiteness in the same way adjectives before nouns do.

So:

• Mobilabonnementet er nyt = correct

But before the noun, with a definite meaning, you would say:

• det nye mobilabonnement

So the difference is:

• before the noun: det nye mobilabonnement
• after er: mobilabonnementet er nyt

Er is the present tense of at være, meaning to be.

It corresponds to English am / is / are, but Danish does not change it depending on the subject:

• jeg er = I am
• du er = you are
• han er = he is
• vi er = we are

So Mobilabonnementet er nyt literally has the structure:

• subject + is
  • adjective

No, this is the normal basic word order for a statement in Danish:

• Mobilabonnementet = subject
• er = verb
• nyt = subject complement / adjective

So it follows the familiar pattern:

• The mobile subscription is new

If you turn it into a question, the verb comes first:

• Er mobilabonnementet nyt? = Is the mobile subscription new?

No. Danish nouns are not capitalized just because they are nouns.

It is capitalized here only because it is the first word in the sentence.

So:

• Mobilabonnementet er nyt. but
• Jeg synes, at mobilabonnementet er nyt.

This is different from German, where all nouns are capitalized.

A helpful mini-pattern is:

Noun:

• et mobilabonnement = a mobile subscription
• mobilabonnementet = the mobile subscription
• mobilabonnementer = mobile subscriptions
• mobilabonnementerne = the mobile subscriptions

Adjective:

• ny = common singular
• nyt = neuter singular
• nye = plural / definite attributive form

Examples:

• en ny telefon
• et nyt mobilabonnement
• nye telefoner
• det nye mobilabonnement

That is why Mobilabonnementet er nyt is the correct form here.