Re: Ryu, kai, and kan
To me, it all depends on what you want conveyed, hence the choice of words used. Shioda sensei named his dojo after his dad's judo dojo that was connected to his house as a kid. Hence the word kan (building) being used in Yoshinkan.
Aikikai was more concerned about the group of guys following Osensei. They all had differences in their techniques or understanding but not that far apart. They valued their association with the founder hence the word kai being used.
Ha to me means version. So Ono-ha Itto-ryu translates to Mr. Ono's version of Itto-ryu.
Ryu to me means style and that there is no deviation. Iwama-ryu is the same no matter where you learn it unlike Aikikai which will have differences amongst it's dojos.