She couldn't send a non-channelling DF because they wouldn't be able to hide as effectively (no invisibility or illusions), and they would have a much harder time trying to find what she wanted since they'd have no experience with *angreal and wouldn't know what to look for. If the goodies were warded (which seems likely) they wouldn't be able to get through the wards.

If she sent a BA, she would have to allow them to see inverted weaves and gateways, neither of which any BA knows how to do at this point. That sort of knowledge might make her BA pawn more dangerous and more likely to get ambitious, which Graendal generally discourages in her underlings. The only way to keep a BA pawn from learning the travelling/inversion/invisibility etc weaves would be to either kill them after they were done, which would cost her a BA, or compel them, which would also cost her a BA because Graendal's brand of compulsion turns people into empty husks and her BA would never be able to pass herself off as normal at the tower again. A BA might also be tempted to steal some of the *angreal for herself. Plus most AS have little knowledge of *angreal (Elayne and Avi are the only ones with any real ability in that direction) and might not even recognize a male angreal. Which of course would be the most likely type for Rahvin to have.

Anyway, for those reasons, using a DF would have a low possibility of success, and using a BA would be too risky and probably still be unsuccessful. Going herself is both low risk and carries a good possibility of success, so going herself was the logical choice.

She knew that Rand would be occupied fighting Rahvin, and thus unlikely to be pawing around in the dustier corners of the Palace. Logically, from her point of view, he'd have Asmodean either with him fighting, or would have left him behind in Cairhien if he didn't trust him enough. Either one would take him out of Graendal's way. Plus, she can still disguise herself with inverted weaves and hide her ability to channel. And if all else fails, she can defend herself just fine if someone /does/ happen to stumble across her, which is exactly what she did.

Yeah, I don't really get that either. Any of the Forsaken could have plundered the Tower (or the Great Holding in Tear), but for some reason none ever did, even the ones who lived in or controlled those places at the time. Both places were warded, but surely they could have gotten through the wards. Maybe they felt the risk of detection was too great. Maybe the DO ordered them to leave those things there. I dunno.

Other Forsaken are lazy about the details, but not Graendal.

It was mostly opportunism to kill Asmo. Why bother with a sudden disguise when he's already seen you? It's not like he's going to forget what he just saw. Better to kill him with a quick dose of balefire, plus that way you leave no witnesses AND kill a competing Forsaken. It's win win!

Well, Graendal /did/ hate him, or at least have good reasons for wanting him dead. She didn't go there specifically to kill him (or anyone), though. He was just a lucky, unplanned, bonus.

Well, yeah. What would a normal person's thoughts be upon turning a corner and seeing a Forsaken? "Shit, I'm dead!" or something along those lines, I'm guessing. If you're a Forsaken yourself - a captive one who's shielded such that you can barely channel - and suddenly an uncaptive, unshielded, rival Forsaken pops up around the corner, what would you expect his thoughts to be? He knew he was a goner.

Sure she would. Graendal's a quick thinker. Why not seize the opportunity to take out some of the competition? Compulsion would have taken too much time and left her vulnerable to detection if she's searching for *angreal with a Compelled Forsaken-disguised-as-gleeman trailing along behind her. He had no knowledge valuable enough for her to bother taking him captive. So, balefire. She had no option to kill Moggy and Cyndane because they belonged to Moridin, and killing the pets of the DO's favorite Nae'Blis is not a smart move.