1. Neo = "new" In the 19th century, Neo-Shinto groups like Tenrikyo or Omoto-kyo emerged, independent religious organizations/cults, usually headed by a charasmatic founder who had an individual revelation. Their doctrines were at variance with orthodoxy (State, Imperial and folk Shinto) and might have included material from other traditions or religions.
2. I think Ueshiba was clear that one didn't have to be an Omotokyo follower to do his aikido - he had his own distance from Omotokyo, unlike Inoue Noriaki, for example. However, I do think that Ueshiba believed that to do HIS aikido, one had to live ANALOGOUS to his "spiritual" way. (Note in Tohei K.'s interview, Ueshiba's distress at observing Tohei, still hung-over after a debauch, doing "ki tricks.") As I wrote, however, in "Aikido is Three Peaches," I think it is clear that he regarded most people's work in aikido as merely contributing energy to the greater spiritual work of the avatars. (But one could BE an avatar. Read the revised version of the essay when the book comes out
3. I think it's simplistic to talk about two ways of aikido - there are, perhaps, a lot. My interest, however, is Ueshiba Morihei's aikido as "opposed to" any and all the other modern versions that don't, apparently, give access to the power he had. For example, Tomiki "had" it - whether, btw, he did solo training like Ueshiba did or not. Shioda apparently "had" it, etc. Whether to the same degree or greater or lesser - - ????? I don't KNOW that solo practice, a la Ueshiba is/was the only avenue to such power as he had. Evidently, even those few of his students who "had" it didn't pass it on to many or any. Similarly, were I exploring Daito-ryu, I would only be interested in the Daito-ryu that gave the very few individuals access to intrinsic power, not the vast majority who are just doing human origami joint-locks by the numbers.
4. Personally, I think this idea of Ueshiba-ha Daito-ryu is kind of silly, much like claiming Christianity is just Judaism. (Using that as a metaphor, Takumakai is almost equivalent to the "Judaizing" churches that maintained a clear connection through ethnicity and ritual to Judaism, churches that were rejected by the more universalist creed that became Catholicism. Thus, Hisa could accept an eighth dan from Ueshiba, and call what he did "aikido." A practitioner of both has informed me that Takumakai is very similar in it's technical parameters to Yoshinkai, not surprising in that both were born in the 1930's). When you go beyond or change to a certain degree, it warrants a name change.
4. Sagawa, Horikawa and Ueshiba EACH made their own unique changes to Daito-ryu. The former two obviously did not see their changes as so significant as to warrant a name change.