A couple questions

She made the mistake of playing with a OUIJA board alone, giving the demon an opportunity. Also, I think the demon wanted to get close to Father Karris.

One of the people there is an astronaut. I forget whether that's mentioned in the movie, but it's in the novel.

1) It chooses her because she is stressed out from her parents split and is playing with the Ouija Board. There is an old idea in the supernatural that kids around her age are more receptive to the paranormal because of puberty and the stress it causes. She might have just been an easy target because of a whole bunch of reasons coinciding at once but there isn't a clean-cut answer just suggestions in the film.

2) She isn't talking to the Father in that scene but to the astronaut who was talking about going into space a few moments before.

1. basically a random choice but one factor would be she could be used to lure Father Merrin as the demon wanted revenge after being defeated in their previous encounter (In Africa).

2. Regan is speaking to the astronaut that Father Dyer was talking to earlier in that party scene. BTW, The astronaut is at the center of the story in The Ninth Configuration. Blatty wrote and directed that movie. It's a very good movie but not really a horror film. Blatty also wrote and directed Exorcist 3. Another very good movie and quite scary IMO.

"What meaning does this have? Was it intended for Father Dyer to die? At the end of the film, we see him alone. Is there still a chance something might happen to him?"

Question is answered in The Exorcist III