Þegar ég kom heim, vissi ég ekki hvort ég ætti að kaupa spínat eða hvítkál, svo ég keypti bæði.

Because Icelandic is a V2 language in main clauses: the finite verb usually comes in the second position.

Here, the sentence starts with the time clause Þegar ég kom heim. That whole clause counts as the first element, so the main clause begins with the verb:

• Þegar ég kom heim, vissi ég ekki ...

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

• Ég vissi ekki ... = I didn’t know ...

So this is a normal Icelandic word-order pattern after an opening clause or adverbial phrase.

Þegar means when.

It introduces a subordinate clause:

• Þegar ég kom heim = When I got home

This works much like English when in a sentence such as When I got home, ....

In Icelandic, heim is often used by itself to mean homeward / home after motion verbs.

So:

• koma heim = to come home
• fara heim = to go home

You do not usually need a preposition here.

A useful contrast is:

• heim = home, toward home (motion)
• heima = at home (location)

So:

• Ég kom heim. = I came home.
• Ég er heima. = I am at home.

Here hvort means whether.

It is used for an indirect question, especially when there is a choice between alternatives:

• hvort ... eða ... = whether ... or ...

So:

• hvort ég ætti að kaupa spínat eða hvítkál
• whether I should buy spinach or cabbage

English sometimes uses if in similar situations, but Icelandic normally uses hvort for this kind of whether/or meaning.

Yes, eiga often means to own / to have, but it also has another important use.

With að + infinitive, eiga can mean something like:

• to be supposed to
• to ought to
• should

So:

• ég á að kaupa = I am supposed to buy / I should buy
• ég ætti að kaupa = I should buy / I ought to buy

In your sentence, ætti is the form used because the speaker is talking about a past moment of uncertainty: I didn’t know whether I should buy ...

Ætti is the subjunctive past form of eiga.

This is common after expressions of uncertainty, doubt, or indirect questioning in the past, such as:

• ég vissi ekki hvort ... = I didn’t know whether ...

So:

• hvort ég ætti að kaupa ... literally means something like
• whether I should buy ...

A rough comparison:

• á að = am supposed to / should
• átti að = was supposed to
• ætti að = should / ought to / would be supposed to, often with a more uncertain or conditional feel

In this sentence, ætti fits the idea of not knowing what the right choice was.

Because in this construction, eiga takes að + infinitive.

So:

• eiga að kaupa = should buy / be supposed to buy

This is just how the expression works in Icelandic.

Compare:

• Ég á bók. = I have a book.
  Here eiga means have/own, so there is no infinitive.

• Ég á að kaupa bók. = I should buy a book.
  Here eiga að + infinitive is the modal-style expression.

Yes. They are the direct objects of kaupa (to buy), so they are in the accusative case.

However, in this sentence their forms look unchanged:

• spínat
• hvítkál

That is because these are neuter singular nouns, and for many neuter nouns the nominative and accusative singular are identical.

So even though the case is accusative, you do not see a different ending here.

Bæði means both here.

Since the speaker ended up buying both things mentioned before, Icelandic can simply say:

• ég keypti bæði = I bought both

Here bæði refers back to spínat and hvítkál.

You may also see bæði in the pattern:

• bæði X og Y = both X and Y

For example:

• Ég keypti bæði spínat og hvítkál. = I bought both spinach and cabbage.

In your sentence, the shorter stand-alone bæði is enough because the two items were already named.

Here svo means something like so, therefore, or then.

In this sentence:

• ..., svo ég keypti bæði.
• ..., so I bought both.

It links the earlier hesitation with the final action.

Depending on context, svo can have several meanings in Icelandic, including:

• so
• then
• as
• very (in other structures)

But in this sentence, so / therefore is the natural reading.

Yes. In fact, your sentence already has that pattern:

• hvort ég ætti að kaupa spínat eða hvítkál

That is literally:

• whether I should buy spinach or cabbage

The eða is the or part. Icelandic does not need any extra word beyond this; the structure is already complete and natural.

Yes.

• koma = to come
• kom = came

So:

• ég kom heim = I came home / I got home

English often says got home, but Icelandic naturally uses came home here.

Yes—this sentence shows several very common Icelandic patterns all at once:

1. Subordinate clause first

   • Þegar ég kom heim = When I got home

2. Verb-second in the main clause

   • vissi ég ekki rather than ég vissi ekki

3. Indirect question with hvort

   • hvort ég ætti ...

4. Modal-like use of eiga að

   • ætti að kaupa = should buy

5. Simple result clause with svo

   • svo ég keypti bæði = so I bought both

So it is a very useful sentence for learning Icelandic word order and clause structure.