If her fiance is a US citizen and meets some other requirements (certain amount of residency in the US) his daughter can be registered as a USC at the embassy and could travel with a US passport to the US. Google CRBA (Consular report of Birth Abroad). If that hasn't been done then it might be hard for her to travel.
If he's not a USC he cannot petition for a fiance to immigrate to the US.
It's true that the other things he is saying seem odd, both the timeline and the idea that a case that far along would not have a case number, or multiple case numbers. Does she trust him generally? Does she think he knows what he's talking about?
It IS a confusing process, if he has good intentions but genuinely doesn't understand the process perhaps he should join her and read up on it.
