My Karate teacher said that if we do the Karate Kata slowly we are doing tai chi, do you agree?
No, what you are doing is Slow Karate. Moving slowly does not make t’ai-chi. T’ai-chi ch’uan is a specific art form with a different conceptual base. Speed has nothing to do with it, as there are fast forms of t’ai-chi ch’uan too. Some styles of karate do have slow forms and training methods but those are considered karate training.