Ik heb een wond aan mijn vinger, want ik sneed me tijdens het koken.

Because Dutch uses hebben to say that someone has an injury or condition.

• Ik heb een wond = I have a wound
• Ik ben gewond = I am injured

Both are possible in Dutch, but they are not exactly the same:

• Ik heb een wond aan mijn vinger focuses on the wound itself.
• Ik ben gewond sounds broader and more general: I am injured.

Wond means wound. It is a general word for an injury to the body.

In this sentence, because the speaker cut their finger while cooking, English might more naturally say:

• I have a cut on my finger

Dutch can also use more specific words, for example:

• een snee = a cut
• een wond = a wound, more general

So een wond aan mijn vinger is correct, though in everyday speech een snee in/aan mijn vinger may sound even more specific.

With injuries, marks, pain, and similar things on body parts, Dutch often uses aan.

So:

• een wond aan mijn vinger = a wound on my finger
• pijn aan mijn arm = pain in my arm / pain in my arm area

This does not translate word-for-word into English. English often uses on or in, but Dutch commonly uses aan in this kind of context.

Sometimes yes, but the meaning shifts a little.

• aan mijn vinger usually means the injury is on/at the finger
• in mijn vinger can suggest in the finger itself, more inside it

For a normal cut, aan mijn vinger is very natural.
If you want to emphasize that the cut went into the finger, in mijn vinger can also make sense.

Because want links two main clauses, and in Dutch it is normally preceded by a comma.

Here the two clauses are:

• Ik heb een wond aan mijn vinger
• want ik sneed me tijdens het koken

This is very similar to English:

• I have a wound on my finger, because I cut myself while cooking.

Want means because, but it works differently from omdat.

With want:

• it introduces a new main clause
• normal word order stays the same

So:

• ..., want ik sneed me tijdens het koken

With omdat:

• it introduces a subordinate clause
• the verb goes to the end

So you could also say:

• Ik heb een wond aan mijn vinger, omdat ik me tijdens het koken sneed.

Both are correct, but the grammar changes:

• want → normal main clause order
• omdat → subordinate clause word order

Both are possible, but they are different tenses.

• ik sneed me = simple past / imperfect
• ik heb me gesneden = present perfect

In Dutch, the simple past is often used in storytelling or when giving background information:

• I have a wound on my finger, because I cut myself while cooking.

The perfect tense is also very natural in speech:

• Ik heb een wond aan mijn vinger, want ik heb me tijdens het koken gesneden.

So the sentence uses sneed because it tells the cause as a past event.

Because snijden is a strong verb, so it does not form the past tense with -de or -te.

Its main forms are:

• snijden = to cut
• sneed = cut
• gesneden = cut

So:

• Ik snijd brood. = I cut bread.
• Ik sneed me. = I cut myself.
• Ik heb me gesneden. = I have cut myself / I cut myself.

Me is the unstressed object form of mij and is very common in everyday Dutch.

So:

• ik sneed me = I cut myself

You could also hear:

• ik sneed mij

That is grammatically correct, but less common in everyday speech.

Mezelf is possible when you want extra emphasis:

• Ik sneed mezelf = I cut myself

In a normal sentence, me is the most natural choice.

No. Snijden can be used both with and without a reflexive pronoun.

Examples:

• Ik snijd brood. = I cut bread.
• Ik sneed de tomaten. = I cut the tomatoes.
• Ik sneed me. = I cut myself.

You use the reflexive pronoun only when the action is done to yourself.

Literally, it means during the cooking.

But in natural English, it usually becomes:

• while cooking
• during cooking
• while I was cooking

So in Dutch:

• tijdens het koken = during cooking / while cooking

Because het koken is a nominalized infinitive: the verb koken is being used like a noun.

Dutch often does this:

• het eten = the eating / the food / eating
• het lezen = reading
• het koken = cooking

So:

• tijdens het koken literally = during the cooking

This structure is very common after prepositions.

Yes, often it can.

• tijdens het koken = during cooking
• bij het koken = while cooking / in the course of cooking

In many everyday situations, both are possible.
Tijdens sounds a bit more explicitly temporal: during.
Bij can feel a bit more like in the activity of or while engaged in.

In this sentence, tijdens het koken is perfectly natural.

Because the speaker means one finger:

• mijn vinger = my finger

If more than one finger were injured, Dutch would use the plural:

• aan mijn vingers = on my fingers

This works just like English.

Yes. A few natural alternatives are:

• Ik heb een snee in mijn vinger, want ik heb me tijdens het koken gesneden.
• Ik heb een wond aan mijn vinger, want ik heb me gesneden tijdens het koken.
• Ik heb tijdens het koken in mijn vinger gesneden.

These differ slightly in wording and emphasis, but all are normal Dutch.

A useful distinction is:

• wond = wound, general injury
• snee = cut, specifically a cut made by something sharp

So if the speaker cut their finger with a knife, een snee is very precise.
Een wond is still correct, but broader.

That means:

• Ik heb een wond aan mijn vinger = correct
• Ik heb een snee in/aan mijn vinger = often more specific and everyday for this situation

Yes. After want, Dutch keeps normal main-clause word order.

So:

• want ik sneed me tijdens het koken

This is normal because:

• ik = subject
• sneed = finite verb
• me = object
• tijdens het koken = time expression

If it were omdat, the order would change:

• ..., omdat ik me tijdens het koken sneed.

That is an important difference between want and omdat.

Yes. Dutch is flexible with adverbial phrases like this.

For example:

• Ik sneed me tijdens het koken.
• Tijdens het koken sneed ik me.
• Ik heb een wond aan mijn vinger, want tijdens het koken sneed ik me.

All of these are possible. The exact word order depends on emphasis and style, but the original sentence is completely natural.