When entering the sanctuary why was natsuki teleported(before the second death there Frederica tells him that she didn’t place any trap and says something about some oath, I am not sure how the oath and the teleport are related), emilia fell asleep as she was a demi human but why was Subaru teleported to the ruins where the trial takes place and then he immediately gets an audience with Echidna.

I don't think the reason for Subaru being teleported is given in the anime, I think it will be explained in cour 2.

if the Satella killed echidna why is she inside Subaru

Echidna isn't inside Subaru. She is inside a world which can be considered as a dream world.