Ulykken kan være dødelig.

Ulykken is the definite singular form: the accident.

• en ulykke = an accident
• ulykken = the accident

So this sentence refers to a specific accident, not just accidents in general.

• Ulykken kan være dødelig. = The accident may/can be fatal.
• En ulykke kan være dødelig. = An accident can be fatal.

Yes. In Bokmål, ulykke is a noun that can be treated as feminine, but many speakers also use the common/masculine-style forms.

So you may see:

• en ulykke – ulykken
• ei ulykke – ulykka

Both are possible in Bokmål, depending on style and dialect preference. The sentence you were given uses the very common form ulykken.

Kan is the present tense of kunne.

In this sentence, it expresses possibility, so it means something like:

• can
• may
• might be able to

So Ulykken kan være dødelig means that the accident may be fatal or can be fatal. It does not mean that the accident is definitely fatal.

Because after a modal verb in Norwegian, the next verb normally comes in the bare infinitive, without å.

Common modal verbs include:

• kan = can
• skal = shall/will
• vil = want to / will
• må = must
• bør = should

So:

• kan være = can be
• må gå = must go
• vil spise = wants to eat / will eat

Not:

• kan å være
• må å gå

Those are incorrect in standard Norwegian.

Være means to be. It is used with an adjective to describe a state or quality.

Here:

• ulykken = the accident
• kan være = can be / may be
• dødelig = fatal / deadly

So the structure is:

subject + modal verb + være + adjective

This is very common in Norwegian:

• Maten kan være god. = The food can be good.
• Situasjonen kan være vanskelig. = The situation can be difficult.
• Ulykken kan være dødelig. = The accident can be fatal.

Yes, but in this sentence the form dødelig is the correct one.

Here dødelig is a predicate adjective: it comes after være and describes the subject.

With predicate adjectives in Norwegian:

• singular subjects often use the basic form
• plural subjects usually take -e

So:

• Ulykken er dødelig. = The accident is fatal.
• Et stoff kan være dødelig. = A substance can be fatal.
• Skadene er dødelige. = The injuries are fatal.

So in your sentence, ulykken is singular, and dødelig is correct.

It is an adjective.

It describes ulykken by saying what kind of state it is in: fatal.

After være, Norwegian uses an adjective, just like English:

• The accident is fatal
• Ulykken er dødelig

So dødelig is not an adverb here.

The normal order is:

Subject + finite verb + infinitive + complement

So here:

• Ulykken = subject
• kan = finite verb
• være = infinitive
• dødelig = complement/predicate adjective

Norwegian main clauses usually follow the V2 rule, which means the finite verb comes in the second position.

That is why this sentence is:

• Ulykken kan være dødelig.

If you move another element to the front, kan still stays in second position:

• I noen tilfeller kan ulykken være dødelig.
  = In some cases, the accident can be fatal.

That would make the sentence general, not specific.

• Ulykken kan være dødelig. = The accident may be fatal.
  This points to a particular accident.

• En ulykke kan være dødelig. = An accident can be fatal.
  This is a general statement.

So the difference is mainly specific vs. general.

These are similar, but not identical.

• kan være dødelig = may/can be fatal
  This expresses possibility.

• er dødelig = is fatal
  This states it more directly as a fact.

• kan bli dødelig = can become fatal
  This suggests a change or development over time.

Examples:

• Skaden kan være dødelig. = The injury may be fatal.
• Skaden er dødelig. = The injury is fatal.
• Skaden kan bli dødelig uten behandling. = The injury can become fatal without treatment.

A rough guide:

• ulykken: stress on the second syllable
  Approx.: u-LYK-ken

• kan: short, like kahn but shorter

• være: roughly VEH-reh / VÆ-re

• dødelig: stress on the first syllable
  Approx.: DØ-de-lig

A few useful pronunciation notes:

• y in ulykken is a Norwegian vowel that does not exist naturally in English.
• ø in dødelig is also a special Norwegian vowel. It is somewhat similar to the vowel in French peur or German schön, depending on accent.
• The kk in ulykken makes the preceding vowel short.

If you want, a teacher or dictionary audio is especially helpful for y, ø, and æ, since English spelling-based guesses are often misleading.