The original alien was carrying the elements to Earth (or so the bad guys thought) to give them to the priest. The bad guys blew up the alien, leaving only hand. The Earth scientists resurrected alien in the form of Leeloo. Bad guys (Mr Shadow, to be precise) have been shown to be able to spy on radio conversations, so it made sense to send alien to tell the priest where the real elements are in person, instead of giving him a call that could be intercepted and real elements taken.
Leeloo was coming to priest to tell him where the stones are. The aliens knew that the evil planet will show up soon, they probably were in contact with priests so they knew who the current priest was. Why does reconstructed Leeloo know who is current priest? Because technology to reform bodies is good enough to restore memories from partial body sample, even if the reconstructed body is that of Leeloo and not Mondoshawan body