Etter frokost feier jeg smuler av bordet og ned i søppelbøtta.

Because Norwegian main clauses follow the V2 rule: the finite verb usually comes in the second position.

Here, Etter frokost is placed first, so the verb feier must come next:

• Etter frokost feier jeg ...

If you started with the subject, then you would get:

• Jeg feier smuler av bordet etter frokost.

Both are correct, but when you move Etter frokost to the front, the verb has to move in front of jeg.

In Norwegian, names of meals often appear without an article when speaking generally:

• etter frokost = after breakfast
• før middag = before dinner
• til lunsj = for lunch

If you say etter frokosten, it usually sounds more like after the breakfast / after that specific breakfast. So etter frokost is the most natural general phrasing here.

Feier is the present tense of å feie, which means to sweep.

A few useful forms:

• å feie = to sweep
• feier = sweep / am sweeping / do sweep
• feide = swept
• har feid = have swept

So feier jeg means I sweep or I am sweeping, depending on context.

Smuler is the indefinite plural form: crumbs / some crumbs.

• smuler = crumbs
• smulene = the crumbs

In this sentence, the speaker is talking about crumbs in a general sense, not a specifically identified set of crumbs, so smuler is natural.

You could say smulene if the crumbs were already known from the context.

Because av often means off a surface, while fra is a more general from.

With sweeping, av bordet is the natural choice because the crumbs are being moved off the table's surface:

• feie smuler av bordet = sweep crumbs off the table

Fra bordet is not impossible in all contexts, but here av is the normal, idiomatic preposition.

Ned i means down into. It emphasizes direction of movement.

That fits very well with the action of sweeping:

• av bordet = off the table
• ned i søppelbøtta = down into the trash bin

If you said only i søppelbøtta, the meaning would still be understandable, but ned i sounds more vivid and natural for this kind of motion.

Because they mean the table and the trash bin.

In Norwegian, definiteness is usually shown by an ending on the noun:

• bord = table

• bordet = the table

• søppelbøtte = trash bin
• søppelbøtta = the trash bin

So Norwegian often uses a noun ending where English uses the.

Because søppelbøtte is a feminine noun, and in Bokmål the definite singular feminine form often ends in -a:

• ei søppelbøtte = a trash bin
• søppelbøtta = the trash bin

In Bokmål, many feminine nouns can also take the common-gender form -en, so you may also see:

• søppelbøtten

Both are possible in Bokmål, but søppelbøtta is a very common and natural form.

Because both phrases belong to the same action feier.

The structure is basically:

• feier
  • smuler
    • av bordet
      • og ned i søppelbøtta

In other words, the speaker is doing one sweeping action that moves the crumbs:

1. off the table
2. into the trash bin

English works similarly: I sweep crumbs off the table and into the trash bin.

After the verb, Norwegian often puts the object before prepositional phrases showing place or direction.

Here the pattern is:

• feier = verb
• smuler = object
• av bordet = where from
• og ned i søppelbøtta = where to

So the sentence is built very naturally as:

When? Etter frokost
What do I do? feier
What? smuler
From where? av bordet
To where? ned i søppelbøtta

Yes, but it changes the feel slightly.

• Etter frokost = after breakfast, in a general everyday sense
• Etter frokosten = after that specific breakfast

And:

• smuler = crumbs / some crumbs
• smulene = the crumbs

So the original sentence sounds like a natural general description of a routine. Using the definite forms would make it sound a bit more specific and context-dependent.