He SEES a man channeling. Who the hell did he think he was serving? As for the fainting, since that is the last mention of him, we have no way of knowing the motivation, only what Rand assumes. It is just as likely that he fainted with fear that Rand might find out his secret. He went from serving a Forsaken to playing courtier to the man who slew that Forsaken. It is easy to take the One Power and its capabilities for granted as readers, but how is Elgar supposed to know that Rand has no way of supernaturally finding out his true allegiance or even the fact of how closely he served Rahvin. He is only a minor lord and in a precarious position - he has few resources to defend himself with and even if he knew what Rand was thinking - that Rand might have had to let the nobles continue to walk free and weild power even if he did know they were Darkfriends - that would almost certainly not apply to the likes of Elgar. Rand might need Arymilla or Elenia or Jarid or Nassin to run Andor and keep it peaceful, he might need to keep them under his thumb to stand for Elayne one day, but he has no need of the likes of Elgar, and Elgar almost certainly knows it. If Rand found a whole nest of Darkfriends among the nobles of Rahvin's court, Elgar would be a prime scapegoat for Lir and the others to blame and offer up for execution to maintain the fiction that Rand has purged their ranks. In short, Elgar has many reasons to be afraid and on the verge of fainting every time Rand mentions Rahvin: surprise over his master's identity is the least of them. And that is assuming it's not an act. And as I noted, Comar seemed to know whom he served. If he didn't know the man's name, he almost certainly knew he served one of the Forsaken, or should have been able to extrapolate as much from just the fragments of their conversation which Mat overheard.

Did you SEE his only interaction with a minion, in aCoS? Carridin was hardly a member of Sammael's inner circle and clearly not trusted or valued beyond his utility, but he openly shows his face.

He almost certainly used Compulsion to make himself first among the High Lords of Tear, who would not have meekly stepped aside for a newcomer, no matter how wealthy or apparently skilled he seemed to be. Given that, why should he fear revealing his identity to those he can trust as long as he Compells them to not expose or otherwise betray him? There is absolutely nothing to indicate his character is akin to Moghedian and the other skulkers among the Forsaken - rather, by seizing power right out of the gate, he gives every indication of being bold and decisive. He was also a general and a skilled personal combatant, suggesting that though he weaves his nets, he doesn't do so from hiding - he goes right out and gets his hands dirty. Rahvin is similarly bold and flagrant, and HE thinks Bel'al is too rash and impatient. Not the kind of man to conceal his identity. And let us not forget, Moiraine DID find out! You give no reasons aside from your assessment of his character on very scanty evidence, for your belief that he would be cautious and careful in concealing his identity. His carelessness is a good assumption after the fact, just as is the case of when someone's property is stolen.

Maybe they were likely, and maybe he did. Why would Rahvin not ward his room against ALL eavesdropping? Though the Forsaken might be his most dangerous adversaries, most of what he is doing in Andor is the sort of thing he tries to conceal from mundanes. After all, they all seem to know plainly what he is doing: he calls himself Gaebril and uses secret operatives to avoid alerting the general public. Given that, it would make much more sense for him to ward against ordinary hearing than One Power eavesdropping if he had to choose, but we see plainly that even relatively ignorant contemporary channelers do not need to choose. Plainly, Rahvin did not bother with wards, so why do you assume Bel'al did? For all we know, it was his fate that started making everyone else take what precautions we see later.

And then, once again, you have to look at subsequent events. Bel'al set a trap for Moiraine! He obviously KNEW she was in the city and where she was staying! For all we know he DID have wards, and she tripped them. You say that Mat's eavesdropping is very different from whatever methods Moiraine would use, and you are right - anything Moiraine was doing on purpose would almost CERTAINLY be much more effective than Mat's accidental overhearing. And let's not forget, there were three ta'veren in the city: who is to say that Moiraine could not have a similarly fortuitous accident? Rand, Mat, Perrin, Nynaeve, Egwene, Elayne, Aviendha, Rhuarc, Darlin, Lan, Thom, Faile & Juilin Sandar were all in the same town for the first and last time in the entire series! Not one other event has seen all of these characters who are all obviously part of the Age Lace the three ta'veren are weaving gathered in the same place. Plainly, this was one of those crucial occasions where the Pattern was overtly forcing events. Moiraine's discovery of Bel'al's identity was what motivated her decision to go into the Stone on the very night Rand needed her. If ever there was a time for a lucky break, it would have been this.