De er forlovet.

It can actually be ambiguous in writing, because the word is at the beginning of the sentence, where de would be capitalized anyway.

• If the meaning you were shown is they, then this is just ordinary de at the start of a sentence.
• If the intended meaning is formal you, that can also be written De in traditional polite style.

In modern Norwegian, the formal De is uncommon in everyday speech and writing. Most of the time, people use du instead.

At the start of a sentence, Norwegian capitalizes the first word, so de becomes De automatically.

That means capitalization alone does not prove that this is the formal pronoun. You need context or the provided meaning to know which one it is.

Er is the present tense of å være, which means to be.

So the structure is very close to English:

• De er forlovet = They are engaged / You are engaged (formal)

In this sentence, forlovet functions like a predicate adjective after er.

A useful way to learn it is as the expression å være forlovet, meaning to be engaged. Historically, it is related to a past participle, but for most learners the practical point is simply that it describes a state.

After er, Norwegian normally uses the predicate form, and here that is forlovet:

• De er forlovet.

You may see forlovede in other contexts, especially before a noun or when used more like a noun:

• de forlovede = the engaged couple / the engaged ones

So forlovet is the normal form in this sentence.

No. Forlovet means engaged, not married.

Compare:

• De er forlovet. = They are engaged.
• De er gift. = They are married.

So forlovet is the stage before marriage.

You normally use med:

• Hun er forlovet med Lars.
• De er forlovet med hverandre.

So Norwegian uses med (with) where English uses to.

A very common way is:

• De ble forlovet.

Here ble is the past tense of bli (become), so it expresses the change into that state.

For learners, this is a very useful contrast:

• De er forlovet. = they are engaged
• De ble forlovet. = they got engaged

No. This is the basic Norwegian main-clause pattern:

• De
  • er
    • forlovet
• subject + verb + complement

So in this sentence, Norwegian works very much like English.

Yes, if the meaning is They are engaged, it is completely natural.

If it is meant as formal You are engaged, that is grammatically possible, but it sounds very formal or old-fashioned in modern Norwegian. In everyday language, people would usually avoid formal De.