Jeg må fylle ut jobbsøknaden i kveld.

Må is a modal verb expressing necessity or obligation—“must” or “have to.” You use må when something is required or unavoidable.
By contrast, skal can also express obligation (“shall,” “will”) but is stronger for planned or scheduled actions (“I will…”) or when giving commands.
Example:
• Jeg må gå til legen. (I have to go to the doctor – it’s necessary.)
• Jeg skal gå til legen i morgen. (I will go to the doctor tomorrow – it’s a plan.)

In Bokmål, you normally write the verb fylle (to fill) and the particle ut (out) as two separate words: fylle ut (to fill out). This is called a separable verb. When you conjugate or combine it with a modal like må, you keep them apart:
• Jeg må fylle ut…
Some dictionaries list utfylle as a single infinitive, but in everyday writing and speech you separate it.

The ending -en on jobbsøknaden is the definite singular suffix in Norwegian (equivalent to “the job application”). Norwegian typically attaches the definite article to the end of a noun.
Breakdown:
• søknad = application
• –en = the (definite suffix)
Together: søknaden = the application.

Norwegian often inserts a linking s when forming compounds. Here:
• jobb (job) + søknad (application) → jobbsøknad (job application).
Then you add the definite ending: jobbsøknaden (the job application).

i kveld literally means “in evening,” but it’s the standard way to say tonight in Norwegian. It’s written as two words:
• i = in
• kveld = evening
It’s fixed in this form—don’t write ikveld.

Yes. Placing i kveld first still respects V2:
• I kveld må jeg fylle ut jobbsøknaden.
This often adds emphasis on i kveld (“Tonight, I have to…”). You can also say:
• Jeg må i kveld fylle ut jobbsøknaden.
All are grammatically correct; you only shift the focus.