I'll answer what I can, but anyone that knows better can feel free to correct me.
1) I think the hidden people were responsible for his disappearance, likely in the same manner of most of the other missing persons, in that they enchanted/hypnotized him and tried to use him to disable the lunar ray, and he ran into the crazed astronauts.
2) Their whispers seem to send the listeners into a trance, so not really crazy, but easily suggestible.
2-bis) The hidden people, when he called them.
3) There was background noise on the tape he'd recorded when he found Bo Murphy listening to a hidden person, and that noise matched a background noise he heard on Olav's recording.
4) The ray was based on his research, but I don't think the government got to him before the hidden people did.
5) I'm not totally sure here...but I don't think so. I think they came to the Earth in the lander, and the lunar eclipses were the times they tried to find people to shut down the lunar ray.
6) Again, I'm not totally sure, but I think they were trying to get back in the lander to get back to the moon.
7) Another I don't have a clear answer for. He was locked in because he'd been chosen, but I'm not sure if that was to keep him from escaping, or to use him as untouchable bait for the Brotherhood to lure the gnomes out.
8) The eclipse caused the lunar ray to malfunction, thus causing it to affect the two astronauts.
9) The Brotherhood was watching her(remember, Bjorn was just across the street), and likely had threatened her that if any outsiders(especially Nelson) returned, she was to turn them away.
10) That's what I understood.
11) I don't think the hidden people were actually angry, despite how Bjorn interpreted the sudden disappearance of the Brotherhood members. They were just getting desperate, and started enchanting more people more frequently.
12) Nelson thought it was important to summon the hidden people because Olav had done so, and he wanted to know what happened to Olav. While he was under their control, the exact details of what happened to him isn't known, but somehow, he ended up at the lander, surrounded by motionless FBI agents, in nothing but his hat, boxers, and a sock, whispering about puzzles.
13) Yes, Ed Davis faked his death after the Hermes II mission was scrubbed, and took up a new life as Isaac Davner.
14) The discovery of the Hermes II was probably the main reason the government tried to come in and take over. Getting the lunar ray back after it was thought lost became a big priority.
15) Alfred was drawn off by the hidden people.
16) Yep, that's correct. The hidden people just need help, and the crazed astronauts were the real 'villains'.