1) translated correctly as Hong Meiling
2) translated as Kurenai Mizuzu
3) translated as Red Mizuzu, which I find even more hilarious.
Her name is actually Hong Meiling,
transliterated into Japanese as "ホンメイリン" (Hon Meirin), which is how ZUN refers to her.
Translated into Japanese, two kun readings for 紅 (hong) are "akai" and "kurenai", both meaning red. Flipping between on and kun readings of characters and their double meanings, along with multilayered transliteration, is just one of the things Japanese Touhou fans do, intentionally ('for the double meaning lulz') or unintentionally (lack of foreign language literacy).
By the way, 紅 can also be read as "momi", and is used in 紅葉 "momiji" (fall colors, or the Japanese maple).