Who is Alexander Waverly?
He is the number one of U.N.C.L.E.'s Section One, and chief of the New York regional office. Based on "The Summit-Five Affair," it appears he is the most senior of the five regional chiefs and, at the very least, first among equals.
In the pilot episode, it's a designation for a woman communications officer who keeps in contact with Napoleon Solo as he carries out his assignment. After that, it is a frequency for U.N.C.L.E. communication devices. It is not the only communications channel, but the one most frequently referenced, usually at the start of a transmission. "Open Chanel D," is what an agent often says when starting such a transmission.
Were there any recurring enemies for Solo and Kuryakin?
Not many. Gervaise Ravel and Harold Bufferton were the agents' primary foes in two first-season episodes (the story was originally devised as a two-part episode but instead was presented as two related, but separate stories). Dr. Egret, a Thrush master of disguise, appeared in two first-season episodes. And G. Emory Partridge (George Sanders) appeared in first- and second-season stories. For the most part, however, the U.N.C.L.E. agents lacked an arch-enemy.