In your question about if there are any kata's in aikido. Well the style I practice Yoshinkan Aikido is taught to the Tokyo riot police, and is a very hard style of aikido. We practice kihon dosa at the begining of every lesson which is I suppose a kata. In this we practice the fundamental basic movements in aikido in a non stop kata form. The whole class practices it in time bothe in left and right kamae. This allows 'shuchu ryoku' to be developed or focused power in the hips, making ones tecnique very powerful.
You will find many differences in styles of Aikido. One piece of Advice I would give is try to stick to a school of Aikido which has as close a lineage to the main schoold of aikido as possible. Im not saying your style isnt any good I dont know the style you practice but try to stick to schools like Yoshinkan, Aikikai, Ki etc etc