So if a detective has not KOSed me of any sort, but attempts to kill me with an incen, am I allowed to kill them or do I actually have to be KOSed and dmged by em to actually kill em?
Sadly you can not. They have not done anything to you in order to damage them. Even if they toss the incen. When in doubt, wait til the detective damages you to kill them.
Like the incen has already went off and has dmged me, putting me at 59hp, am I allowed to kill them then, or still no?
If you are 100% sure that the Detective threw the incen then yes you may kill but be careful in manner of this style of gameplay.
If they KOS you and then throw an incendiary, frag, or discombomb (When you are near a ledge) at you, would that permit you to shoot them before you are damaged, since it is clear they are attempting to damage you and have called the KOS?
This would be the same situation as calling a kos on you then shooting at you but missing, you still have the right to kill the detective in the situation you described.