1.It was a "shinkage-ryu jujutsu menkyo" There is no evidence of Takeda studying any such system. That's why I state my belief that it was simply a symbolic recognition of a special relationship (not unlike Takeda drawing up a new certificate called Daito-ryu menkyo kaiden for Hisa Takuma several decades later.
This may be true in the main, but incorrect in particulars. If the scroll displayed here
is indeed the Shinkage-ryu menkyo given to Ueshiba by Takeda, it is purely a (Yagyu) Shinkage-ryu document. It is a copy of the Shinrikyo (Shoe Offering Bridge) scroll, the first part of Yagyu Munenori's famous Heiho Kadensho.
Before I explain further, let me give a rough outline of YSR history for context. (Not for Ellis, of course, but for others.) Shinkage-ryu was founded by Kamiizumi Hidetsuna, and taught Yagyu Munetoshi. Munetoshi's fifth son Munenori went on to serve Tokugawa Ieyasu as a kenjutsu instructor, gaining influence and power as he served Ieyasu's son and grandson. Eventually he became a daimyo. His son, Mitsutoshi, aka Jubei, is also famed as a swordsman. Munenori's line of the Yagyu family is known as the Edo Yagyu.
As famous as Munenori and his sons were, the mainline of YSR was actually passed on to Munetoshi's grandson Toshitoshi, aka Hyogonosuke. Hyogonosuke eventually came to serve the lords of Owari as a kenjutsu instructor, in what is modern day Nagoya. His line of the family came to be known as the Owari Yagyu, and it is this line that maintains Yagyu Shinkage-ryu to this day.
I mention this because the Shinrikyo is a purely Edo Yagyu document. It was not used by the Owari Yagyu or their students. It was written by Munenori for his deshi and descendants, and was used to recognize someone as a member of the ryu. In this sense, it was not a menkyo in the sense of license, or even as a certification of attainment. It was a document indicating affiliation.
I make this point because it would seem that Gejo Kosaburo was a student of the Owari Yagyu line of YSR, not the Edo Yagyu line. If Takeda had learned YSR from Gejo, it's unlikely he would have then given Ueshiba this Edo Yagyu document. Nor would it be related to Jikishinkage-ryu, since YSR and JSR branched away from each other in the founder's generation.
The document is a curious one. The contents, as much as I can read, are taken directly from Heiho Kadensho, but it is not a faithful copy. I believe the image in the above link has been edited to show the beginning and the end of the scroll (thus obscuring any possible references to actual YSR kata in the original), but in the section is shown, three of the five points regarding stance ("stand in hitoemi", "lower your shoulder to your opponent's fists", and "extend your left elbow") are omitted, leaving only "Use your fists as a shield" and "support your body with your front leg, and extend your rear leg".
The lineage preceding Takeda's signature runs:
Kamiizumi Musashi-no-Kami Fujiwara Hidetsuna
Yagyu Tajima-no-Kami Taira Munetoshi
Yagyu Tajima-no-Kami Taira Munenori
Over Ten Generations in Old Aizu Domain
Takeda Sokaku Minamoto Masakazu
The Aizu domain reference is no abbreviation on my part, that is literally what it says in the document. That's how Takeda basically links himself to Munenori -- generations of anonymous Aizu bushi. Had Takeda not been illiterate, I would assume that he copied, or had it copied, out of a book that published the Heiho Kadensho. As it is, it still seems highly suspect that he didn't even write the name of his direct teacher.
Of course, there seems to be no other indication that Takeda studied Yagyu Shinkage-ryu. The above site quotes from Shishida Fumiaki's book "Aikido Kyoshitsu" that (according to Tomiki, I assume) Ueshiba had never seen a fukuro-shinai until he came to Tokyo, and that when visiting the Kobukan one day, Takeda came across a fukuro-shinai and went ballistic.
So, while the densho is not one for some form of Shinkage-ryu jujutsu, I nonetheless agree with Ellis's idea that this was some symbolic gesture from Takeda. Where Takeda got the exemplar for the scroll is a mystery. Perhaps, like Ueshiba's dabbling in judo, Tenjin Shin'yo-ryu and Yagyu Shingan-ryu, Takeda had briefly studied with some former Aizu-han instructor of YSR, long enough to receive a scroll indicating membership in the ryu, but not long enough to really take much from it before moving on to Itto-ryu and Jikishinkage-ryu. Perhaps he simply obtained the densho as an historical document (the Meiji era being a good time for folks to sell old, obsolete densho for some ready money), and knew only that it was a kind of scroll indicating affiliation.
Interestingly, Shishida says that Gejo taught Ueshiba various kata, except for Muto, which is not taught until the deshi received inka, the highest level of certification. That fits with YSR practice. The Sho-Chiku-Bai aikiken kata that Ueshiba taught Hikitsuchi are taken from Sangaku En-no-Tachi and Kuka-no-Tachi, two of the "Omotedachi" of Shinkage-ryu -- the lower level kata a YSR deshi first learns. However, Ueshiba apparently did not take from Empi, the third Omotedachi. The kata for Sangaku and Kuka are listed in the Shinrikyo, but Empi is not. I wonder if Ueshiba's training with Gejo basically involved Gejo showing him these kata listed on this scroll Takeda gave him, which Takeda never actually taught.