In de keuken snijd ik een tomaat en eet ik een sinaasappel.

Dutch often puts a time or place phrase first to set the scene or give it emphasis. Here, In de keuken means in the kitchen, and it tells you where the actions happen before the speaker mentions the actions themselves.

So this sentence is not unusual at all. It is a very normal Dutch way to say:

In the kitchen, I cut a tomato and eat an orange.

This is because Dutch main clauses usually follow the V2 rule: the finite verb comes in the second position.

In this sentence, the first position is already taken by In de keuken, so the verb must come next:

• In de keuken = position 1
• snijd = position 2
• ik = after the verb

So:

• In de keuken snijd ik een tomaat
• not In de keuken ik snijd een tomaat

The same pattern appears in the second part: eet ik.

Because en eet ik een sinaasappel is treated as a second coordinated clause, and Dutch normally keeps the subject in that clause too.

So the structure is roughly:

• In de keuken snijd ik een tomaat
• en eet ik een sinaasappel

Repeating ik makes the sentence sound balanced and clear.

If you start with the subject instead, Dutch often allows omission of the second ik:

• Ik snijd een tomaat en eet een sinaasappel.

But in the sentence you were given, the repeated ik fits the inverted word order after the fronted phrase In de keuken.

Yes. It applies to both snijd ik een tomaat and eet ik een sinaasappel.

So the meaning is:

• I cut a tomato in the kitchen
• and I eat an orange in the kitchen

Dutch often mentions a shared setting once at the beginning instead of repeating it.

Because keuken is a de-word in Dutch.

Dutch nouns take either:

• de
• or het

You usually have to learn this with each noun.
So:

• de keuken = the kitchen

There is no special grammar reason visible from this sentence alone; it is simply the correct article for keuken.

Een means a/an, so it is used for a nonspecific item:

• een tomaat = a tomato
• een sinaasappel = an orange

If you said de tomaat or de sinaasappel, it would sound like you mean a specific one already known in the conversation:

• de tomaat = the tomato
• de sinaasappel = the orange

So the sentence presents them as ordinary, unspecified items.

The verb is snijden = to cut.

For ik in the present tense, Dutch usually uses the stem of the verb:

• snijden → stem snijd
• ik snijd

So the spelling comes from the verb stem.

A useful extra point: at the end of a word, Dutch d is often pronounced more like t. So snijd may sound very close to snijt, but it is still spelled with d because of the verb’s base form snijden.

Yes. That is also a correct and very natural Dutch sentence.

Compare:

• Ik snijd een tomaat en eet een sinaasappel.
• In de keuken snijd ik een tomaat en eet ik een sinaasappel.

The difference is mainly focus:

• starting with Ik focuses more on the subject
• starting with In de keuken focuses more on the place

So both are grammatical, but they present the information differently.

It is in the present tense.

• snijd = cut / am cutting
• eet = eat / am eating

In Dutch, the present tense can describe:

• something happening right now
• a habitual action
• a general statement

So depending on context, the sentence could mean either:

• I am cutting a tomato and eating an orange in the kitchen
• or In the kitchen, I cut a tomato and eat an orange

A natural past-tense version would be:

In de keuken sneed ik een tomaat en at ik een sinaasappel.

Here:

• snijd → sneed
• eet → at

Both are irregular past-tense forms.

A rough English approximation is snide, with the sn- clearly pronounced at the beginning.

A few notes:

• ij often sounds somewhat like the vowel in English eye
• final d is often pronounced like t
• so snijd sounds close to snijt, even though it is spelled with d

This is only an approximation, but it is a useful one for beginners.