Okay so i killed Caeser but the NCR seems to think he is still alive, as do legionaires i hunt down and kill, why is this?

I don t know most NPCs in NCR know as soon as you do it. If you are wearing faction armour that may have something to do with it.

CL should be trying to kill you.

three questions:

What were you wearing?
If you were wearing some kind of faction armor, they won't know you did it (so I've heard).

Are you sure YOU killed him and not your companion?
If your companion killed him, they won't acknowledge his death (as my experience).

Did you let him die or kill him during surgery?
If you did, everyone will think he died naturally and not by your hand.