I know someone who has a foreign passport but a Permanent Resident status in the USA. And they had to get their visa to come to Nevis. I think that visa is only valid for a few months. But when you arrive, MUA will send your passport (on the orientation day) to the office in Nevis and it will be stamped with a long term visa for the duration of your studies on the island.
Concerning the ticket, many students buy theirs on kayak.com.
Hope that helped