Can someone explain shutter island please?

So I have some questions regarding the story

If we’re to believe Teddy is insane and is actually Andrew then this is all a ruse created by the warden. At the end Andrew accepts his reality and has a lobotomy.

However there are things I don’t get.

I don’t understand the two Rachel’s, the first is found by the Wardens, the second in a cave. If this is planned by the wardens why are there two?

Secondly why does chuck further go along with Teddy’s delusions. Why does he during the storm add that the asylum is funded by the house of un American activities and that the asylum wanted him there

Why is the lunatic allowed to hurt him? If this was planned by the hospital why add this risk?

Why does the patient write run on his book. If she was part of the game why would she do this?