Sy vra watter peper ek wil hê.

Watter means which.

It is used when you are choosing from identifiable options, like which pepper.

Wat usually means what, not which:

• Wat wil jy hê? = What do you want?
• Watter peper wil jy hê? = Which pepper do you want?

So in this sentence, watter is the right word because it points to a choice among peppers.

Because watter already acts as the determiner.

In English, we also say which pepper, not which the pepper. Afrikaans works the same way here:

• watter peper
• not watter die peper

So watter already introduces the noun, and no extra article is needed.

Yes, wil on its own means want or wish to, but wil hê is a very common Afrikaans way to say want in the sense of would like to have.

So:

• Ek wil gaan = I want to go
• Ek wil koffie hê = I want coffee / I would like coffee

In your sentence, ek wil hê means I want in the sense of choosing or wanting to have a particular pepper.

Because the part after vra is an embedded question, and Afrikaans pushes the verbs to the end in subordinate clauses.

The embedded clause is:

• watter peper ek wil hê

Compare:

• Main clause question: Watter peper wil ek hê?
• Embedded question: ... watter peper ek wil hê

So hê goes to the end because this is not a direct question; it is a clause inside a larger sentence.

Because this is a subordinate clause, not a main clause.

In a main clause or direct question, Afrikaans often puts the finite verb earlier:

• Ek wil dit hê.
• Wil ek dit hê?
• Watter peper wil ek hê?

But after a word like vra introducing an indirect question, the subordinate clause takes a different word order:

• Sy vra watter peper ek wil hê.

So ek comes before the verb cluster, and the verbs move toward the end.

The whole sentence is a statement, not a direct question.

It means that she is asking something, but the sentence itself reports that fact. So it ends with a full stop.

Compare:

• Direct question: Watter peper wil jy hê?
• Reported/embedded question: Sy vra watter peper ek wil hê.

English does the same thing:

• Which pepper do you want?
• She asks which pepper I want.

Only the first one normally takes a question mark.

Vra means ask.

Here it introduces the reported question:

• Sy vra ... = She asks ...
• ... watter peper ek wil hê = which pepper I want

So the sentence structure is:

• main clause: Sy vra
• embedded question: watter peper ek wil hê

This is very common in Afrikaans with verbs like vra, weet, sê, and wonder.

Yes, effectively it is the base verb form used after the modal wil.

After modal verbs such as kan, moet, sal, and wil, Afrikaans normally uses the main verb in its plain form, without te:

• Ek wil eet.
• Ek kan kom.
• Ek moet werk.
• Ek wil dit hê.

So hê is the verb form that follows the modal wil.

The circumflex in hê helps show that it is pronounced with a long, marked vowel.

It also helps distinguish it from other forms and makes the word easier to recognize in writing.

For a learner, the important practical point is:

• hê = the verb to have

You should learn it as a fixed spelling, especially because it appears very often in expressions like:

• wil hê
• het
• gehad

Here Sy means she.

At the start of the sentence it is capitalized because it is the first word, not because it is a different form.

So:

• sy vra = she asks

Afrikaans sy can also be a possessive form meaning his in other contexts, but here that is impossible because it is followed by the verb vra, so it must be the subject pronoun she.

Yes. The direct-question version would be:

Watter peper wil jy hê?
or, if keeping I as the subject,
Watter peper wil ek hê?

The sentence you were given is the reported or embedded version:

• Sy vra watter peper ek wil hê.

That is a useful comparison because it shows the word-order change:

• Direct question: Watter peper wil ek hê?
• Embedded question: watter peper ek wil hê

So if you know the direct question, the embedded form becomes much easier to understand.