Efter flytten har vi fortfarande en stor kartong i köket.

Because flytten is the definite form of flytt.

• en flytt = a move
• flytten = the move

In Efter flytten, Swedish is saying after the move.
That sounds natural when both speaker and listener know which move is being talked about.

This is a very common Swedish pattern: the definite article is usually added as an ending:

• en bil → bilen
• ett hus → huset
• en flytt → flytten

Swedish often puts a time phrase or context phrase first. Efter flytten sets the scene before the main statement.

So the sentence structure is:

• Efter flytten = time/context
• har vi fortfarande... = main clause

This is very normal in Swedish, just like English can say:

• After the move, we still have...

Starting with Efter flytten gives a little emphasis to the timing.

This is because of the Swedish V2 rule (verb-second word order).

In a main clause, the finite verb usually comes in the second position. If something other than the subject comes first, the verb still has to stay second.

So:

• Vi har fortfarande en stor kartong i köket. = subject first, then verb

But if you move Efter flytten to the front:

• Efter flytten har vi fortfarande en stor kartong i köket.

Now Efter flytten takes the first position, so har must come next, and vi comes after it.

This inversion is very important in Swedish.

Fortfarande means still.

In this sentence, it comes after the verb:

• har vi fortfarande

That placement is very natural in Swedish.

Compare:

• Vi har fortfarande en stor kartong i köket.
• Efter flytten har vi fortfarande en stor kartong i köket.

So fortfarande often appears after the finite verb and subject in a main clause.
It works a lot like English still, though the exact placement is not always identical.

Because kartong is a common-gender noun, so it takes en.

• en kartong = a box / carton

The adjective stor is the basic common-gender singular indefinite form:

• en stor kartong

Compare:

• en stor bil
• ett stort hus

So here:

• en because kartong is an en-word
• stor because the noun is singular, common gender, and indefinite

It actually is already in the form it needs.

Swedish adjectives change depending on gender, number, and definiteness. Here the noun phrase is:

• singular
• common gender
• indefinite

So the adjective form is stor:

• en stor kartong

Compare:

• ett stort paket
• två stora kartonger
• den stora kartongen

So stor is the correct form specifically for en + singular indefinite noun.

Because Swedish usually expresses definiteness by adding it to the noun itself.

• ett kök = a kitchen
• köket = the kitchen

So i köket means in the kitchen.

You only add a separate word like det in certain structures, for example with adjectives:

• i det stora köket = in the big kitchen

But without an adjective, i köket is enough.

Because i means in, and for rooms in a house Swedish normally uses i.

So you say:

• i köket = in the kitchen
• i vardagsrummet = in the living room
• i badrummet = in the bathroom

På is used in other situations, such as:

• på bordet = on the table
• på jobbet = at work
• på landet = in the countryside

For a room like a kitchen, i is the normal choice.

Yes, absolutely.

That version is also completely correct:

• Vi har fortfarande en stor kartong i köket.

The difference is mainly emphasis and flow:

• Vi har fortfarande... = neutral statement
• Efter flytten har vi fortfarande... = adds the time context first

So both are good. The original just highlights after the move.

Not always.

Kartong usually refers to a cardboard box/carton.
Låda is a more general word for box, drawer, or container depending on context.

So:

• en kartong = often specifically a cardboard moving box or carton
• en låda = a box more generally

In a moving context, kartong sounds very natural because people often mean a cardboard packing box.

Yes. Har is the present tense of ha (to have).

So the sentence is describing a current situation:

• har vi fortfarande = we still have

It is not the perfect tense here.
This is just the ordinary present-tense verb ha used in the sense of possession.

Because Swedish usually puts the at the end of the noun as a suffix.

So instead of a separate word like English the, Swedish often uses endings:

• flytten = the move
• köket = the kitchen

This is one of the biggest differences from English.

Very roughly:

• English: the kitchen
• Swedish: kök-et

A helpful breakdown is:

• Efter flytten = adverbial/time phrase
• har = finite verb
• vi = subject
• fortfarande = adverb
• en stor kartong = object
• i köket = place phrase

So the pattern is:

Time phrase + verb + subject + adverb + object + place

This happens because of Swedish verb-second word order. If the sentence began with the subject instead, it would look like this:

• Vi har fortfarande en stor kartong i köket.

That may be easier to recognize at first.