You mean while Rand wandering around felt observed?

There were 15 warders there, they would likely have sensed the presence of Shadowspawn in the Keep (the alarm was indeed sounded early, as if warders gave some sort of forewarning) unless they were warded (which is possible, but unlikely with many non-BA arond who would have puzzled out the critters had been warded...). Most of all it's really not obvious to rationalize why Slayer, a Grey Man or a Fade needed to spy on Rand at that time. Ishamael had plenty of agents in place keeping track of things... Ingtar, Tomas, Verin, Liandrin, Alviarin to name but some of the obvious ones.

Two we know for sure had the task (one of many) of making sure Rand remained in the Keep and "safe" were Ingtar and Liandrin (the fact after freeing Fain Ingtar went straight for Rand, gettinghim out of Shadowspawn's way and encouraging him to go to the now empty and safe dungeon where another agent of the Shadow, Liandrin, "stood guard" is extra evidence the Grey Man later couldn't possibly have been targeting Rand (unless it was instructed to miss, merely an incentive for Siuan and co. to decide Rand needed protection and change their minds about letting him go, maybe). Otherwise the target had to be Siuan Sanche. Having just reread those scenes, it's pretty heavily foreshadowed the BA wanted her out of the way... after trying to forestall the Blue from sending two sisters close friends of Moiraine to support her, after trying to divide the Blue's allies by insinuating Siuan wasn't acting for the whole Tower but pursuing a secret Blue agenda with Moiraine, Black Sitters broke further with all tradition (and law, according to Moiraine) by attempting to deny Siuan the right to lead and even be part of the embassy, which nearly worked. But having failed to stop her, they surrounded her with Black sisters, including not only the Head of the Black in person, but also one friendly to Moiraine and Siuan, Verin, who brought to them, no doubt as ordered, the Black Prophecy meant by Ishamael as "a threat" (and "something else" RJ didn't want to tell us about) to their attention, and interpreted for them what Ishamael most likely wanted them to interpret (it's the "something else" RJ didn't want to tell us... I think he feared he'd point to obviously to Verin being BA if he explained Ishamael used the DP to pass specific information... attract the Tower's attention on the Seanchan, Isam for Lan, warn Lanfear had entered the "game".) and seemingly keeping to herself on purpose the one thing the Shadow hoped might convince Lan to ask to remain behind as Moiraine travelled back with sisters and 14 warders to TV.. It's Verin who conveniently puzzles out the extremely obscure clues pointing to Hawkwing's armies having landed in Falme yet seems to have messed up with her orders by attempting to convince Siuan she didn't believe in Hawkwing's armies and she should push that whole thing out of her mind... the Toman's Head stuff is a topic Liandrin also brought to Moiraine's attention (and which was talked already in TV, but disbelieved) - and from the way she's surprised to have talked this was one of Ishamael's compelled orders Liandrin wasn't aware of...) managed to wriggle herself into one of their secret conversations (and who's much suspected of being a member of the SC too).

Rand isn't the only one who felt someone observing him. Liandrin felt it too when she got out of Amalisa's rooms. She felt an itch and someone observing her and turned around to find no one.

I'm not sure what RJ was getting at with this (it could for instance have been Rand having the DO's attention or something like this), but the one character with "an habit" of skulking around spying unseen like this is Lanfear (and it would make sense she spied/protected Rand in Fal Dara, and spied on Liandrin trying to puzzle out what Ishamael was up to). There's no flash of white dress to give her away to us this time (too early in the book for this), but otherwise what happens there is very similar to the TDR scenes with her (the brief flash of white dress seen by Egwene outside Verin's rooms, and how she vanished in the WT (IRRC, one of the girls run after Else and bumps into Lanfear who has let down her MoM and she mistakes her for a sister, who soon vanishes), and for that matter the scene at the end of TGH (with Min). Lanfear has a "disappearing trick" of some kind, most likely an inverted weave variant of the more primitive weave Rand uses to make Egwene invisible in Cairhien. There would be not "jumping around" to explain if it's simply Lanfear with weaves to make her invisible and silent as she take the opportunity Rand was alone to come observe him up close. She could have been just a few feet from him.

It would make sense Lanfear did that, when she appeared as Selene she seemed to know quite a bit already about what to expect of his entourage, not to mention all she already knew in TDR to hatch her plot to send the girls to Tear. If it was her in those scenes she would have seen Mat, Perrin and Loial (when Rand comes on them is when his "follower" leaves), and possibly some of his interaction with Egwene, Nynaeve.

The "wind", actually a wall of air, in the first chapter is probably Lanfear as well. It seems to me to have been an attempt to place him in a situation to use saidin, if he could. As Selene later in the Mirror World she repeats the same pattern, except this time it's not just to avoid a wooden sword and humiliation, she put him in fake "life-threatening danger". It's all very logical, considering it's one of the few known ways in which sparkers usually begin to channel (another is a secret desire to... that's how Moiraine had her first touching, playing at being ASa with her stone).

In the early books, RJ seemed to like sticking to "patterns" for the Forsaken. It's the threads to spot and follow to figure out who's behind what. Until TSR all Grey Men and Myrddraal are sent by Ishamael (who also uses dreamshards/nightmares a lot), Lanfear's the one who skulks around, is either invisible or in disguise and who interacts with Rand's entourage and messes with the pawns of the other Chosen - and who sends dreams/messes with dreams, Rahvin uses only DFs, Be'lal relies on Liandrin's BA, Sammael's the one sending critters (DH) etc. In the first three books RJ kept it all relatively simple, just a bit more complex in books 4-5 and it's really only from LOC on all hell breaks lose and RJ really toyed with confusion (and to introduce some of the behind the scene stuff from earlier books) and creating a feeling of Shadow-paranoia to echo Rand's. It comes at the time the reader (like Rand) are now "on their own", having lost Moiraine's guidance (and misguidance, as until the end of TDR when RJ wanted to mislead us, he had Moiraine misinterpret things knowing we relied on that character and came to take anything she stated as fact as the truth.).