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:
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:
Compare:
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:
But after a word like vra introducing an indirect question, the subordinate clause takes a different word order:
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:
English does the same thing:
Only the first one normally takes a question mark.
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:
You should learn it as a fixed spelling, especially because it appears very often in expressions like:
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:
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:
That is a useful comparison because it shows the word-order change:
So if you know the direct question, the embedded form becomes much easier to understand.