Yes, there is a principle of phonetic transliteration: the initial represents the sound in the language of origin. E.g. J. K. Rowling would be "D-zh": "Дж. К. Роулинг".
This leads to such things as English name "Charles" represented as "Ч." (Чарльз, "Ch"), but French name "Charles" as "Ш" (Шарль, "Sh"): "Ч. Дарвин" (Charles Darwin), "Ш. Перро" (Charles Perrault).
Similarly Finnish names with "J" will be represented by "Й" (Joukahainen) and Spanish by "Х" (Juan).
(1) If an author is named Vladimir, would the initial be "В" or "Вл"?
Usual English practice is to do initials purely by spelling. So Sharon Stone would be reduced to S. Stone, not Sh. Stone, even though no S-sound is present in the name.
(This is also the Chinese practice - Shanghai gets abbreviated SH, which feels appropriate until you realize that it's S for shang, H for hai.)
(2) How is Перро pronounced? Would that correspond better to Perrault or Pierrault?
(3) Why is Darwin "transliterated" with в rather than у?
(1) A Russian author may choose how to present his/her name so you may in fact see abbreviations like "Вл." (Владимир) оr "Евг." (Евгений, Eugene) and such. (For instance one of Moscow theaters is officially called "Театр имени Евг. Вахтангова". Here "Евг." is an abbreviation of the founder's name and is rendered exactly in this form.) But this is a part of an artistic expression. (After all, the name may be a pseudonym, so also an artistic creation. There is, for example, "И. Грекова" where the form is chosen because together it sounds like "игрек", Greek I; this is a pseudonym a math professor chose for her non-math writings.)
But a foreign author does not do that, of course. As far as I understand the algorithm is something like that: 1) abbreviate according to the language of origin; 2) see how this abbreviation will sound in that language; 3) represent this sound in Russian. Usually this amounts to looking up a previous decision on that name.
I think this is a common issue in cross-script translation.
(2) "Перро" should be more like "Perrault"; "Pierrault" would be "Пьеро" or "Пьер", more French-sounding.
(3) This is a custom. The sound "w" does not exist in Russian, so there is a choice how to represent it. Most often it is "в", but there is a tradition in rendering it as "у" if it is the first character. And it seems the choice changed over time, so Churchill is traditionally "Уинстон", but the cigarette brand "Winston" из "Винстон". In the middle of word it is almost always "в", but there are exceptions, such as "Хемингуэй" (Hemingway).
1) No, it's just Russian translators are aware that in English, Daniel and John start from different letters and want to indicate that. I think it's the only case of 2-letter initial in English->Russian translation. Can't recall any other cases, but maybe there are such with translations from other languages.
2) like Spanish perro, but accent on the last syllable, "perró". I think Pierrault would add a "soft sign", Пьерро.
3) There's no equivalent of W in Russian, and different translators take different ways - either В (v) or У (u). E.g. I read two translations of Sherlock Holmes with Watson being Уотсон and Ватсон.
Oh, well, correct, Spanish perro would be пэрро. The name Perrault is Перро and it's clear Е, not Э. But Pierrault would be definitely Пьерро, because of the i.
Also, sometimes in borrowed words everyone writes Е like in the original but pronounces Э, especially in the Western part of Russia. IDK exactly the reasons, may be it's just disgust for the letter Э, may be it's Ukrainian and Belarussian orthograhy influence, where Е is pronounced like Э.
This leads to such things as English name "Charles" represented as "Ч." (Чарльз, "Ch"), but French name "Charles" as "Ш" (Шарль, "Sh"): "Ч. Дарвин" (Charles Darwin), "Ш. Перро" (Charles Perrault).
Similarly Finnish names with "J" will be represented by "Й" (Joukahainen) and Spanish by "Х" (Juan).