How to fence corners on a lot that is not square?
Any code I'm aware of doesn't allow permanent structure to block easement. And by privacy you are speaking of stockade style fencing? Just want to be clear.
But your questions: Place post C on the outside or two on the inside if you insist  with each placed flush with end of that section of fence.
For acute angles use scrap to shim angles, or one post per side of angle as close to end of fencing.
For ease of installation and aesthetics, unless there is a particular reason you need a complex corner, I would eliminate post (corner) C completely and consider fencing the angle from B to D. If C is the 10' clearance then set B and D farther away from that corner and don't sweat the minimal real estate lost.