I will try and answer your questions to the best of my knowledge. As I stated I am new to Aikido so I am not well versed yet in all the terms.
1. Fugakukai Aikido has no competitions whatsoever. Even though it is an offsoot of Tomiki-ryu. Karl Geis Shihan believed that the concept of tanto randori had failed as a developmental process in teaching a true and really useful Aikido system. He felt, quote: "That tanto randori, like most sports, by it's rules and nature predicts that the strongest and most athletic person will prevail. Which he believe was not a viable idea if Aikido was to be useful and productive to all who practiced it, large, small, strong, weak. So the techniques that were based on power and/or speed would need to be modified in kata and actual practice in such a way as to make off-balance a realistic part of the technique.
2. As for Fugakukia Judo...all this is, is Kodokan Judo. In fact, you can earn points for rank promotion through competition.
I hope I have answered your questions. If not I would be happy to refer your question to sensei Nick Lowry, 6th Dan.