Ilden er varm.

Because Norwegian usually puts the definite article on the end of the noun.

So:

• ild = fire
• ilden = the fire

That -en ending is doing the job that the does in English.

The base form is ild.

If you look it up in a dictionary, you would normally look for ild, not ilden.
In this sentence, ilden is the definite singular form.

You may also meet different article patterns with some Norwegian nouns depending on style or variety, but for this sentence, ild → ilden is the important pattern to learn.

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

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

Examples:

• Jeg er varm = I am warm
• Du er varm = You are warm
• Ilden er varm = The fire is warm

So er is a very common and important verb form.

Because Norwegian adjectives change form to match what they describe.

Here, varm is used with a singular non-neuter subject, so the basic form is used:

• varm = singular non-neuter
• varmt = singular neuter
• varme = plural

Compare:

• Ilden er varm = The fire is warm
• Huset er varmt = The house is warm
• Bøkene er varme = The books are warm

So varm is the correct form in this sentence.

Because Ilden er varm and den varme ilden are two different structures.

• Ilden er varm = The fire is warm
  Here, varm is a predicate adjective. It comes after er.

• den varme ilden = the warm fire
  Here, varme is an attributive adjective. It comes before the noun.

This is a very common difference in Norwegian:

• after er: ilden er varm
• before the noun: den varme ilden

So the sentence is not missing anything; it is just using a different structure.

Yes. This is the standard word order for a simple statement:

Subject + verb + adjective

So:

• Ilden = subject
• er = verb
• varm = adjective

This is completely normal Norwegian main-clause word order.

Usually varm means warm, but in real use it can cover a range of temperatures depending on context.

In a very literal beginner sentence, varm is fine.
In natural English, people might often say The fire is hot rather than The fire is warm.

Norwegian can also use stronger words when needed, such as het, but varm is the basic everyday temperature adjective.

So the grammar is straightforward even if the exact English wording may vary by context.

Because ild and brann are not exactly the same.

• ild = fire as the substance, flame, or burning element
• brann = fire in the sense of a blaze, accident, or building fire

So in Ilden er varm, ild is the right word, because the sentence is talking about fire itself, not a fire incident.

To make it a question, move the verb first:

• Er ilden varm? = Is the fire warm?

To make it negative, add ikke after the verb:

• Ilden er ikke varm. = The fire is not warm.

This is a useful pattern to remember:

• statement: Ilden er varm.
• question: Er ilden varm?
• negative: Ilden er ikke varm.