Coordinates

I recently completed a re-watch of season 3 and afterward started thinking about the coordinates that Mr C collected. He told his son that he had received 3 coordinates and that 2 of the 3 matched.

So I'm thinking the source of the 3 coordinates were: From Betty (the secretary of Hastings)/Ray. From Tulpa Dianne (who got the coordinates from the photograph of Ruth's arm). From Philip Jefferies during their brief meeting.

So it stands to reason that the first two coordinates matched since Bill/Ruth/Betty were all a team of sorts and what Ruth had is what Dianne had since she just copied from her. But it got me thinking and asking a few questions:

1) Who killed Ruth? If Mr C was in the Zone when Briggs, Bill and Ruth met and killed Ruth, then he could have copied the coordinates from Ruth's arm right then and there (they were impossible to miss). It certainly appears that Mr C killed her since her wound is identical to the gunshot wound when Mr C shot Phyllis in the head. But if Mr C didn't kill her who did? The woodsmen don't use guns, and a gun was clearly what made a wound of that nature (at least that is what is presented to us in the show and what we are to understand).

2) Why was Betty killed? In fact, why was anyone killed who had the coordinates? Mr C was on a mission and only had a day to get it done, it appears that getting the coordinates and getting to where he needed to be was primary. Had he accomplished his mission, he could have always gone back and took care of anyone who fed him the wrong coordinates, in the meantime, keeping them alive might prove valuable if they still had good coordinates and hid them from him.

Of course, other questions are: What coordinates was he looking for - where was it he was looking to go? Did he ever receive the correct coordinates at all? Had he gone up on the rock instead of his son would it have affected him the same? etc.