I think it's clear that Luc and Isam are both alive - something about this is mentioned in the dark prophecies (something like, Isam hunted Luc in the high passes, one died, "yet both live". Also, we get Slayer's POV at one point, and he talks about deciding which identity he will leave TaR as - he can choose, and it seems to be linked to his leaving/entering The Unseen World.

I may be misunderstanding your second point, but: I think it's in the WH murders that Slayer comes out of TaR in one place, murders two people in their bed, and then leaves. I'm pretty positive he can use his ability to jump from place to place (in the same way that Egwene travels to Salidar).

To that end, I admit that it seems off that Slayer didn't just jump out of TaR and straight to some Dark character for healing. Still, he'd just been shot, and he needed to leave TaR immediately so that Perrin wouldn't finish the job. It makes some sense that, in a moment of panic and injury, he would jump to the closest place where he could just get on a horse and split.