I looked it up on here and it said it's possibly Aramaic or derived from the Hebrew name Mahlah. either way, it should be ma-HALL-ia. people have been known to mispronounce their names due to ignorance on their parents' part.
1. yes, I could see Molly as a nn for Mahalia.
2. yes, I can picture Molly on the described girl, though I am not so sure about Mahalia.