Gisselet er redd.

Because gisselet is the definite singular form of et gissel.

• et gissel = a hostage
• gisselet = the hostage

In Norwegian, the idea of the is very often added to the end of the noun as a suffix instead of being a separate word.

Since gissel is a neuter noun, its definite singular ending is -et, giving gisselet.

In Norwegian, you usually do not put a separate word before the noun when the noun is definite by itself.

So:

• gisselet = the hostage

not normally:

• det gisselet

A separate determiner such as det is used in other structures, especially with adjectives, for example:

• det redde gisselet = the frightened hostage

But in your sentence, there is no adjective directly before the noun, so gisselet by itself is the normal form.

Er means is / are / am, depending on the subject.

It is the present tense of the verb å være = to be.

So:

• Gisselet er redd. = The hostage is afraid.

Other examples:

• Jeg er redd. = I am afraid.
• De er redde. = They are afraid.

Because redd comes after er, and after to be-type verbs, Norwegian usually puts the adjective in the same place English does:

• The hostage is afraid.
• Gisselet er redd.

This is called a predicative adjective: the adjective describes the subject through the verb er.

Compare:

• et redd barn = a frightened child
  Here the adjective comes before the noun.
• Barnet er redd. = The child is afraid.
  Here the adjective comes after er.

Because redd is the correct form here for a singular subject in this kind of sentence.

With this adjective, the form changes mainly when you have plural or a definite adjective phrase:

• Gisselet er redd. = The hostage is afraid.
• Barna er redde. = The children are afraid.
• det redde barnet = the frightened child

So in your sentence, redd is correct because gisselet is singular.

Yes. In many contexts, redd can be translated as either afraid or scared.

So:

• Gisselet er redd.

can naturally mean:

• The hostage is afraid
• The hostage is scared

The exact English choice depends on style and context, but the Norwegian word is completely normal here.

You would say:

• Et gissel er redd.

Compare:

• et gissel = a hostage
• gisselet = the hostage

So the only difference is whether the noun is indefinite or definite.

You usually use redd for.

Examples:

• Gisselet er redd for hunden. = The hostage is afraid of the dog.
• Gisselet er redd for å dø. = The hostage is afraid of dying.
• Gisselet er redd for at noe skal skje. = The hostage is afraid that something will happen.

So redd is very often followed by for when you want to name the thing causing fear.

Because this is a normal Norwegian statement:

• subject + verb + complement

So:

• Gisselet = subject
• er = verb
• redd = complement/adjective

This is the standard pattern in simple declarative sentences.

If you changed the order to:

• Er gisselet redd?

that would become a question:

• Is the hostage afraid?

A rough guide is:

• Gisselet ≈ GISS-eh-let
• er ≈ a short unstressed ehr
• redd ≈ similar to English red, but with a Norwegian r

A few useful notes:

• The stress is mainly on the first syllable of gisselet.
• The g in gissel is a hard g, like in go.
• The ss is a clear s sound.
• redd has a short vowel.

The exact pronunciation varies a bit by dialect, but that guide will get you close.