Re: Kata and Aikido
I actually believe that most aikido dojo, even under the Aikikai umbrella, do have kata but don't call it that: For a given attack/technique combination there is an idealized form for both nage and uke, which may be very different from dojo to dojo, but can actually be demonstrated.
Depending on the dojo, it might or might not include specified places to include atemi or where it expected certain balance-taking will occur.
Folks often focus on learning the idealized form for nage. It was suggested early on in my training that I also focus on learning the idealized form for uke because it makes it easier to work w/ newbies with less "mouth waza" by encouraging them to stay with me as I move.