Can Black Ajah have Warders? Would a Warder know if his AS was Black?
The answers are: yes, and depends.
We know BA can have Warders; one of the Greens from Liandrin's posse complained about having to leave her Warders behind when they fled the Tower [TSR: 38, Hidden Faces, 439]. (This may have been Asne Zeramene, who has four Warders (per WH); presumably Jeaine Caide has at least one Warder as well, but Jeaine has been MIA since Tanchico, in TSR, and we don't have any information on her Warders or lack thereof.)
So, given that BA can have Warders, we now need to ask what the deal with Black Ajah Warders is. RJ has said several things on the subject. At a post-TPOD signing in Seattle, he told Kevin Bartlett that the easiest thing would be to pick a Darkfriend for a Warder. At a post-TPOD signing in Pennsylvania, RJ "made some comments about how Warders of the BA might sometimes meet with 'accidents' so the BA can remain secret. Alternatively, BA might intentionally bond Darkfriends." [Melinda Yin] To confirm, Verin reveals that her Warder, Tomas, is a Darkfriend as well. [TGS 39 :A Visit from Verin Sedai]
Finally, at a post-TPOD signing in Northern Virginia, he discussed the topic. John Novak's synopsis: "If an Aes Sedai becomes Black Ajah, the Warder would know instantly that something was up, but wouldn't know exactly what. The Black Ajah has three choices, then - hope the Warder is a Darkfriend or amenable to being one, hide the affiliation, or arrange for an accident. Yes, this would be painful for the Aes Sedai, but it might become necessary. The process of becoming Black Ajah is evidently quite painful in its own right and thus probably involves more than just swearing new Oaths on the Rod. (I submit that this is why the Red Ajah is rife with Black Ajah - they have an easier time actively recruiting from that pool. By the same token, I claim that the Green Ajah is more pure than the others.)"
Eldrith Jhondar (formerly a Brown), we discover in WH, also has a Warder, named Kennit. Kennit was the reason Eldrith, Asne, Temaile Kinderode, and Chesmal Emry were eventually forced to flee Samara, where Moghedien had sent them: "What had sparked the decision to leave was the arrival of Eldrith's Kennit in the town, sure that she was a murderer, half convinced she was Black Ajah, and determined to kill her no matter the consequences to himself" [WH: 10, A Plan Succeeds, 244].
This plus the rest of Asne's POV clears up most of our questions about the BA and Warders. We now know that BA Warders do not necessarily have to be Darkfriends, but that at least some are; one of Asne's Warders, Powl, is a DF, the other three are not. (Note that, apparently, this has not been realized by the non-Black AS. For all the talk of Black Ajah, not a single person has mentioned the possibility of Black Warders.)
We also learn (from both this and from Elayne's POV later) that the Warder bond can be masked, which explains how a BA could do her dastardly deeds while bonded to a non-DF Warder. Asne seems to have no fear that she cannot compel her three non-DF Warders into obeying her, while it's clear that Eldrith has no control over Kennit; likely this is because Asne has never let her masking slip while doing bad things, the way Eldrith did (or because Eldrith is simply not as good at compelling her Warder as Asne is).
Lastly, it appears that while BA will kill their Warders to protect their secret, they are very reluctant to do it. Asne doesn't find it surprising that Eldrith would choose to flee rather than allow Kennit to be killed and suffer the inevitable result.
There has been some indication that the Warders referred to in TSR were murdered. It's possible they were, as long as they were Jeaine's and not Asne's, but Eldrith's behavior makes it less likely to be the case. Plus, since we know that Asne's Warders were (a) left behind, (b) not all DFs, and (c) not killed, it doesn't make sense that Jeaine's would have been, whether they were Darkfriends or not.