Actually it's specifically stated that not many of the wise ones have the capability to dreamwalk. the few that can communicate with the rest.

Rand's suspected first channeling (moiraine's theory) was on Bela (although I'd argue that it could have been egwenes for entirely the same reason, but rand's fits his PoV better).

Asmodean and Lanfear were both traveling across the waste with a merchant caravan (of DOOM!), so one or the other could have been (but wasn't "definitely") in cairhien. Additionally, Lanfear originally told Rand that she was a cairhienian lady (Selene) BUT there was no evidence than anyone in Cairhein knew about it since no one knew who Rand was talking about when he mentioned her.

I would ASSUME that male dreamers could exist. Dreamers in and of themselves are pretty rare (egwene being the only notable non-aiel randlander in some time, with the wise ones being the only others), even amongst people who can channel. (IIRC, channeling isn't required explicitly but it seems to help).

Wise ones get training in it. The majority of males who are potential dreamers are also channellers and thus die or go mad long before they learn the discipline necessary for Dreaming.

IIRC (might be wrong) demandred has spied in t'a'r (on elayne?) which I would assume involved some degree of "using" the environment ("teleporting around") rather than physical sneakiness. Which would make him a Dreamer (albeit a weaker one). And MOST of the male forsaken got punched out early on in the series or weren't inclined that way.

Among the dark, the strong are the only ones to survive. For most of the guys that's a physical/raw power kind of thing (even the more thoughtful ones like demandred who's a general is still VERY powerful), the women (naturally weaker than the men) would only be able to advance by changing the game and being crafty/sneaky. As a general rule among the forsaken, guys lead armies and/or fight directly, the women manipulate from the sides or contribute raw brainpower (mesaana likes actual physics without the application of the power, semirhage knows more about bodies than anyone, graendal is a psychiatrist, etc).

I would agree that rand, rahvin and a few others' access of t'a'r isn't so much "dreaming" as crashing the party, since they're coming in by gateway in physical form. Demandred is the only one that's exhibited anything that might be actual dreaming (and it might not).

Lanfear claimed t'a'r, but Moggy thinks it's hers and uses it a lot. Who is "better" is up for debate (and I lean towards lanfear only because Nynaeve, with minimal training, managed to best the "expert" using rules of her own turf. ouch.) The only person that seems less effective in TAR is birgitte, and even then she was able to spy for a good long time.