Han er tilliten verdig.

It is:

• Han = subject
• er = present tense of å være
• tilliten verdig = a predicative expression describing han

The key point is that verdig is an adjective, and tilliten is the complement connected to that adjective. So this is not a normal English-style worthy of X structure; in Norwegian, verdig can take the noun phrase directly.

Because Norwegian does not need one here.

English says worthy of the trust, but Norwegian often says simply:

• tilliten verdig
• respekten verdig
• all ros verdig

So verdig can connect directly to a noun phrase without a preposition.

Tilliten is the definite form, meaning the trust or the trust in question.

In this kind of sentence, Norwegian often uses a definite noun or some other specific phrase, for example:

• tilliten
• vår tillit
• folkets respekt

Using bare tillit here would sound less idiomatic to many speakers. The sentence is talking about a particular trust, not just the concept of trust in general.

Because that is the usual pattern with this use of verdig.

A very common model is:

• noe/noen verdig

Examples:

• all ære verdig
• respekten verdig
• en konge verdig

So Han er tilliten verdig follows a normal established pattern. Learners should treat X verdig as the standard structure here.

You may occasionally encounter other wordings, but tilliten verdig is the idiomatic model to copy.

Yes. It sounds somewhat formal, written, or elevated.

In everyday speech, Norwegians would often choose something simpler, such as:

• Han fortjener tilliten.
• Han er til å stole på.

So the original sentence is correct, but it has a more polished or literary tone than casual speech.

Yes, like an adjective, it can agree with number.

In your sentence, han is singular, so the form is verdig.

With a plural subject, you would normally get verdige:

• De er tilliten verdige.

A useful thing to remember is that adjectives ending in -ig do not add a separate -t in the neuter singular, so the singular form stays verdig.

You use the object form.

For example:

• Det er meg ikke verdig.
• Det er deg ikke verdig.
• Det er ham ikke verdig.

That is because the pronoun is not the subject of the sentence; it is the complement linked to verdig.

So for a learner, it is safest to think of this pattern as taking an object-form pronoun after verdig.

Yes. This is a productive pattern, especially in formal Norwegian.

Examples:

• Hun er prisen verdig.
• De er all respekt verdige.
• Han var ikke oppgaven verdig.

So once you learn the pattern være + X + verdig, you can use it with many nouns meaning something like praise, trust, respect, a prize, an office, a task, and so on.