It wasn't Ishamael nor anyone connected to him (his Shadowspawn, his DF etc.) because obviously Ishamael had no idea that Fain had reached Falme, so he never learned this from Barthanes, and if he didn't know he had no reason to want to punish the man.

It wasn't Lanfear either. She could have had motive, if she was still around to figure out that a) Rand had gone to Barthanes, b) what Barthanes revealed to Rand about Fain baiting him to follow him and where and c) Barthanes was a DF linked to Ishamael. Killing Barthanes would keep Ishamael in the dark about what happened, then. Also, the murder of Barthanes doesn't fit Lanfear's MO at all (she wouldn't kill so gruesomely except in full blinding rage), and there's no evidence that Lanfear managed to learn anything about the events at the palace (no evidence that when she vanished she remained in Cairhien instead of following Rand from TAR), let alone so fast that she could have had Barthanes killed by the next morning. There's also the problem that Lanfear well knows Ishamael can track ta'veren just like she can, making it rather all pointless because killing Barthanes wouldn't in any way cut the trail for Ishamael (it's the Portal Stone episode which did, for both Lanfear and Ishamael... but shortly after Rand re appeared, they both found him again).

Slayer acting at Lanfear's orders is certainly a possibility. Slayer is a butcher, and it fits the assassination, but there's the same objections about Lanfear, minus the M.O. one.

The one with the best motive to arrange for Barthanes' death and the simplest solution however is Fain himself. He needed Barthanes to pass the message to Rand, but he also needed to cut off his trail and lose the Shadow. He needed a Waygate for this, and this one was guarded by a DF and Fain knew this. The best way to vanish was to leave DF behind (they were all under his SL spell) to kill Barthanes soon after he met Rand. Alternatively, a Myrddraal, but Trollocs can't be trusted for that sort of job. The murder was a butchery, but what else would you expect of DF further tainted by the SL evil? The may have cut Barthanes to pieces because Fain whom they feared like hell told them to make very sure Barthanes was dead. Another possibility, perhaps the more likely of all, is that Fain met with Barthanes in his rooms, and when he left he set a nasty trap (like the "loop" he left in the village, but this one lethal) that killed Barthanes when he got back to his rooms the night of the party.

The gholam is most unlikely. The books pass, and evidence that there's more than one gholam around in the series is as non existant as ever, and less and less likely to surface before the end now. Most likely, there's only one gholam, the one Sammael discovered in a stasis box. It wasn't in service then, and wouldn't be for some time. And yes, I think it's that gholam who killed Fel. Jordan mysteriously said Fel was killed because someone thought he might reveal too much to Rand, but no Forsaken ever seemed alarmed (or to even know) that Rand has asked Fel about the seals, the sealing and the cleansing of saidin. My conclusion is that Sammael had Fel killed and used a gholam, because he thought this mysterious hidden scholar was the disguise Rand hid his teacher Asmodean under. He sent his gholam through the Ways (explains how it got from Illian to Cairhien so fast, explains why there was delay between Sammael's conversation with Carridin and the arrival of the gholam to Ebou Dar, and his "perhaps I can send someone to deal with the AS". "Perhaps", because the gholam was already on his first mission since awakening and not back to him yet? It's what I think) because he thought the man to kill in Cairhien was a Forsaken. A gholam to kill a non-channeller would be complete overkill, so whoever had Fel killed didn't know much what he was dealing with. Moridin for example would have used a Grey Man or a DF assassin to kill an old scholar, as usual (he sent that even against ta'veren...). Sammael would likely have done the same, but he didn't think he was dealing with an old hapless non-channeller. He thought he was dealing with a Forsaken who taught Rand too much and had to die (I think Jordan refused to reveal this straight out, because it would spoil the suspense he managed to create if he told us the Shadow never knew anything about Fel and what he really was revealing to Rand. But the Shadow could hardly know anything... Fel and Rand always had very private conversations with Aiel guarding the door so no spy could learn anything, and exchanged only very obscure messages otherwise)

It also fits with Sammael's hints to Graendal around that time that a nasty Shadowspawn in a stasis box could be a bad surprise for even a Forsaken. It also fits with his comment to Graendal that he was sure Rand had Asmodean hidden somewhere and wanted to find out. I think Rand condemned Fel through his too visible visits, and by the fact he had the Academy work for him on designing weapons. There's an Illianer scholar there, and I think he was a spy for Sammael, who draw all the wrong conclusions and had "Asmodean" killed.