Ég ætla bara að skreppa í búðina og koma strax aftur.

Ætla is the verb to intend / to be going to. In the pattern ætla að + infinitive, it often expresses a plan or near future action.

So:

• Ég ætla að skreppa ... = I’m going to pop out ...
• It can sound like either I intend to... or I’m about to / going to..., depending on context.

In this sentence, it is very natural to understand it as I’m just going to...

Because ætla normally takes að + infinitive.

So the structure is:

• Ég ætla
• að skreppa

That is the standard grammar after ætla.

A good pattern to remember is:

• ég ætla að fara = I’m going to go
• ég ætla að borða = I’m going to eat
• ég ætla að skreppa = I’m going to pop out

Because skreppa and koma are both part of the same idea, joined by og (and).

So the sentence is understood like:

• Ég ætla að skreppa ... og koma ...

The að belongs to the whole infinitive phrase, and Icelandic does not need to repeat it before the second verb.

In other words, this works like English:

• I’m going to pop to the shop and come right back

You do not need to say to again before come in English, and Icelandic works similarly here.

Bara usually means just, only, or simply.

Here it softens the sentence and gives the feeling of:

• I’m just going to the shop
• I’m only popping out for a moment

It suggests the trip is small, quick, and not a big deal. It often helps create a casual, reassuring tone.

Skreppa is a very common verb for making a quick trip somewhere. In this kind of sentence, it often means something like:

• pop out
• nip out
• run to
• make a quick trip

So að skreppa í búðina is more like to pop to the shop than the more neutral to go to the shop.

It sounds casual and often implies that the action will be brief.

Because Icelandic distinguishes between:

• movement into/to a place → often í + accusative
• location in a place → often í + dative

Here the speaker is going to the shop, so it is directional movement. That is why you get:

• í búðina = to the shop / into the shop

Compare:

• Ég fer í búðina = I’m going to the shop
• Ég er í búðinni = I’m in the shop

So búðina is accusative, while búðinni would be dative.

Búðina is:

• búð = shop/store
• plus the suffixed definite article = the shop
• in the accusative singular

Icelandic usually puts the at the end of the noun instead of using a separate word.

So:

• búð = shop
• búðin = the shop
• búðina = the shop (accusative form)

The accusative form is used here because of í with motion.

Because koma is still an infinitive here.

The whole sentence is built around Ég ætla ... and then two infinitives:

• að skreppa
• og koma

So the structure is basically:

• I am going to [pop to the shop] and [come right back]

If you used kem, that would be a fully conjugated finite verb meaning I come, which would not fit this structure.

Strax means immediately / right away, and aftur means back or again depending on context.

Here aftur clearly means back, so:

• strax aftur = right back / straight back / back immediately

So koma strax aftur means come right back.

Yes. The subject ég applies to both actions:

• Ég ætla ... skreppa ...
• [ég ætla ...] koma strax aftur

You do not need to repeat the subject. This is normal in both Icelandic and English when the same person does both actions.

So the full sense is:

• I’m going to pop to the shop and I’ll come right back

even though Icelandic does not repeat ég before koma.

Yes, Icelandic has some flexibility with adverb placement, but the version you have is very natural.

Bara can move in some contexts, but different positions can change the emphasis slightly. In your sentence:

• Ég ætla bara að skreppa í búðina ...

the feeling is I’m just going to pop to the shop...

That placement makes bara modify the whole plan in a very natural way. It sounds casual and idiomatic.

So while other word orders may be possible, this one is a very good, everyday way to say it.