Osan'gar wanted to avoid fighting at the Cleansing, especially after he already confronted Rand twice (once with a fatal result). Reread his reaction, when Moridin announces that the Forsaken have to battle Rand, when he uses the Choedan Kal, and Osan'gar's motive becomes obvious.




It's still just a guess that Taim might know how to reach Slayer, while we know for a fact that all Forsaken have access to him. That makes a Forsaken per se a better suspect for being the patron. The location of the patron's Gateway is really too ambiguous to to be a clue.





It's absurd to believe that Slayer is an unsuccessful assassin, since we learn e.g. that the DO, the Forsaken and high-ranking DF regularly use his services. Of course, also a powerful person like Brigitte remarks on Slayer's dangerousness. That Slayer also killed others under similar circumstanzes like Asmo was killed (namey "out of thin air" ) actually speaks for him being Asmo's killer as well. On the other hand, we never saw e.g. Graendal murder someone. We also see Slayer spying on people and it's clear that at least Luc knows the Caemlyn Palace very well (certainly better than any other suspect in Asmo's murder mystery). Probably he spied on Asmo, waited for a good opportunity and when he saw that Asmo would apparently go alone in a certain direction, Slayer simply went there before him to surprise Asmo. If Asmo hadn't opened the door, Slayer had just waited for another opportunity.

Bashere was already quite quick with his knife, but of course didn't actually want to kill Rand. If Slayer had an even faster and deadlier weapon, e.g. a crossbow with a poisoned bolt, it's very likely that Asmo simply wasn't quick enough to protect himself (as said, if Slayer doesn't anyway have special gifts we don't know about yet to e.g. block a channeler's ability for a moment).