In India, people use the term "fiancee" at least in English and pronounce it [fiˈjæːnsi]
Traditionally, "popping the question" Western-style isn't a thing AFAIK, but some Indian cultures do have engagement ceremonies. I don't think Malayalees traditionally have them, but at least some North Indians do. Their engagement ceremonies can be fairly elaborate and very public, kind of like a smaller version of a wedding ceremony.
When my brother and sister-in-law got engaged (in the Western sense), her mom wasn't satisfied with that, so she threw a party that was supposed to be the engagement ceremony and invited not only our family but also their family friends and ours. It involved lots of food, lots of dancing (the two people who were engaged were definitely required to dance. This is an extremely foreign concept to us South Indians), and IIRC also them feeding sweets to each other and her brother tying a small string, called [ˈɾakʰi]
in Hindi, around his sister's wrist and then another around my brother's. (Usually, I think the fiancee's sister is the one who is supposed to do this, but my sister-in-law doesn't have a sister). In North Indian culture, this string symbolizes fraternity, so in this case, this was supposed to mean that her brother accepted my brother as a second sibling.