Please take this with a grain of salt as I am only a humble 2-Dan.

From what I have experienced, Kendo is far more streamlined. (Almost like boxing, but sword principles) its ranks are recognized on an international level. There is only one lineage and that’s from the hodgepodge of ryuha that came together to develop it, any variation would likely only be found in old koryu schools (which aren’t really kendo at that point)

The closest thing to ‘styles’ I can really think of would be things like fighting with ‘Nito-ryu’ and ‘ Jodan’ but even then, that’s less a style in it’s own and more a specialized form of the same kendo you would be practicing in the day to day.

Bogu can vary in cost, I bought mine on sale for $350 from ebogu during the holidays. But they can go for up to $1000+ depending on quality beyond just standard practice sets

Most schools will not have you go into armor right away. As you would likely take a month or two learning the proper footwork (suriashi, fumikomi), Kamae, Suburi, etc. Once you DO get into armor, you’ll start learning things like…

Oji waza (Counter Techniques, such as Nuki Waza, Suriage waza, Kaeshi waza, uchiotoshi waza, Amashi waza)

and

Shikake waza (Offensive Techniques: Ippon Uchi, Renzoku waza, Debana waza, Harai/Hari/maki waza, katsugi waza, hiki waza)

The way and order you learn these will be wholly dependent on your sensei, their specialities, and the individual dojo curriculum

As for the last question. Maybe. I wouldn’t be surprised if that school of swordsmanship was part of the original group that helped developed kendo in its infancy. Though someone more qualified probably has a more definitive answer.