Hun føler seg svimmel.

Because føler is the present tense form of the verb å føle (to feel).

• å føle = to feel
• føler = feel / feels

So:

• Hun føler seg svimmel = She feels dizzy

Norwegian present tense verbs are often made by adding -r to the infinitive:

• å føle → føler
• å snakke → snakker
• å bo → bor

Seg is a reflexive pronoun. In this sentence, it means something like herself, but in English we usually do not translate it literally.

So word-for-word, the sentence is close to:

• Hun = she
• føler = feels
• seg = herself
• svimmel = dizzy

But natural English is simply:

• She feels dizzy

Many Norwegian verbs use a reflexive pronoun where English does not. With føle seg + adjective, Norwegian expresses a person’s condition or how they feel:

• Jeg føler meg trøtt = I feel tired
• Han føler seg bedre = He feels better
• Vi føler oss klare = We feel ready

Because seg is specifically the reflexive form, used when the subject and object refer to the same person.

• Hun føler seg svimmel = She feels dizzy
  (she is the one experiencing the feeling)

If you used henne, it would mean her as a separate object, not reflexive, and it would sound wrong here.

Compare:

• Hun ser henne = She sees her
  (two different females)
• Hun føler seg svimmel = She feels dizzy
  (the feeling applies to herself)

So after reflexive verbs or reflexive expressions, Norwegian uses meg / deg / seg / oss / dere / seg depending on the subject.

Yes. Both are possible, but they are not exactly identical in emphasis.

• Hun er svimmel = She is dizzy
• Hun føler seg svimmel = She feels dizzy

The version with føler seg emphasizes her own sensation or experience. The version with er states the condition more directly.

Very roughly:

• Hun er svimmel = direct statement about her state
• Hun føler seg svimmel = focuses on what she is feeling

In many situations, both would work naturally.

Svimmel is an adjective, meaning dizzy.

It describes a state or condition. In this sentence, it comes after føler seg, which is very common with adjectives:

• føle seg bra = feel well
• føle seg syk = feel sick
• føle seg nervøs = feel nervous
• føle seg svimmel = feel dizzy

Because adjectives often stay in their basic form after verbs like være (to be) and expressions like føle seg (to feel).

This use is called a predicative adjective. In predicative position, the adjective is often just the dictionary form:

• Hun er trøtt = She is tired
• Han føler seg dårlig = He feels bad
• Barnet er lite = The child is small

So svimmel does not need an extra ending here.

The basic word order is:

Subject + verb + reflexive pronoun + adjective

So:

• Hun = subject
• føler = verb
• seg = reflexive pronoun
• svimmel = adjective

This is normal Norwegian main-clause word order.

It changes to match the subject:

• Jeg føler meg svimmel = I feel dizzy
• Du føler deg svimmel = You feel dizzy
• Hun føler seg svimmel = She feels dizzy
• Han føler seg svimmel = He feels dizzy
• Vi føler oss svimle = We feel dizzy
• Dere føler dere svimle = You (plural) feel dizzy
• De føler seg svimle = They feel dizzy

Notice especially:

• meg for jeg
• deg for du
• seg for han/hun/de
• oss for vi
• dere for dere

Because it is the first word of the sentence.

In Norwegian, as in English, the first word of a sentence is capitalized:

• Hun føler seg svimmel.
• Jeg er trøtt.
• De kommer snart.

But normally hun is lowercase in the middle of a sentence.

It is a very common pattern for talking about how someone feels physically or emotionally.

Examples:

• Jeg føler meg bra. = I feel good.
• Du føler deg trygg. = You feel safe.
• Han føler seg sliten. = He feels tired.
• Hun føler seg ensom. = She feels lonely.
• Vi føler oss klare. = We feel ready.

So føle seg + adjective is a useful pattern to learn as a whole.

A rough English-friendly guide is:

• Hun ≈ hoon but with a more rounded vowel
• føler ≈ something like FUH-ler, though the ø sound does not exist exactly in English
• seg ≈ sigh in some dialects, but pronunciation varies; in many standard descriptions it is closer to sai
• svimmel ≈ SVIM-mel

A few notes:

• ø is one of the trickiest sounds for English speakers. It is a rounded front vowel.
• The g in seg is not pronounced as a hard English g.
• svimmel has stress on the first syllable: SVIM-mel

If you want to sound natural, it helps to learn the sentence as one chunk rather than word by word.

It is neutral and completely natural in everyday Norwegian.

You could use it in ordinary conversation, for example:

• Hun føler seg svimmel etter turen. = She feels dizzy after the trip.
• Jeg føler meg svimmel. = I feel dizzy.

There is nothing especially formal or slang-like about it.