1. In terms of linguistics, I think that "aiki" is possessive of many activities. Activities may not necessarily be possessive of aiki. Specifically, Aiki-do claims that as an activity it is inclusive of aiki. A person with aiki may express that aiki in a variety of activities. In asserting this claim, even here on Aikiweb we regularly post about the expression of verbal aikido or interpersonal aikido. It is therefore possible to say, "I did aikido this morning" and refer to a non-aikido activity possessed of aiki, such as avoiding a conflict with the ol' ball and chain. The fact the language did not explicitly say "verbal" aikido is more an illustration of poor communication.
2. If the curriculum of aikido defines "aiki" then we have two issues:
First, Probably Ueshiba Sensei would've been doing something like Daito ryu Ueshiba Ha or some such offshoot of the parent curriculum (Daito Ryu) as adopted by a single practitioner. Second, a mixed martial artist who is practicing the technical curriculum of aikido would be practicing aikido; or, practicing Ueshiba ha Daito ryu as mentioned before.
Yes. From a principle-based perspective, Aikido shares with many other fighting and body conditioning systems the same core principles we define as "aiki". O Sensei was unselfish of sharing "aiki" and mentioned in several different occassions where he opined that a practictioner he observed was doing aiki. Remember, aikido was neither the only name for what O Sensei taught, nor was it the name O Sensei chose.
I understand aikido has a pressure to define itself and establish itself within the fighting systems. I also understand we are trying to do this with a relatively young curriculum, of which the majority is derived from its parent art. I also understand that a great number of our practitioners are unable to express with clarity and consistency what is aiki. I am not convinced we wish to express our art as a collusion of waza that breaks down when applied within other fighting systems. Rather, I prefer to see it as an expression of aiki, which may be included in the practice of many activities.
This is almost a mirror of the debate over whether the USA's Constitution is a living document or a strict, inalterable code. And sadly, I don't think that there will be a scholarly winner on that debate any time soon, but due to mission creep the Constitution ends up a living document anyway.
It is quite possible that Morihei Ueshiba really did mean aikido, the thing, not the name, as he practiced it, was Daito Ryu-inspired aiki focused through the lens of his spiritual beliefs and Daito Ryu-derived waza. But several generations later, when aikido has grown to encompass a lot more than that strict interpretation of what he was doing, and at its root codified, morphed, and expanded by many others than merely him (and as far as historical evidence says, he wasn't really involved in codifying it anyway), can we put the genie back in the bottle and say aikido is just that anymore, just what Morihei Ueshiba was doing?
As a practitioner and student of aiki (but not necessarily aikido, as I see it) as a technical skill set, I do not dare to claim that by doing so I am doing aikido by that. If I say I do aikido, it is only that I have actually practiced in aikido dojos with a credible lineage to Morihei Ueshiba, and that's even side-stepping the debate about whether those dojos are recognized by the Hombu dojo. As you note, aiki is not unique to aikido either, so it is not a necessary and sufficient condition to really say you're doing aikido just on that count alone. Trying to reestablish aikido as merely the study of aiki is a losing battle, whether or not it ever was.
On that note, it is somewhat laughable to think of aikido waza being applied in any sort of freestyle sparring. 5 minutes of experimentation will yield predictable results in this regard for just about anyone. But aiki? That stuff is dangerous in the hands of an experienced fighter. Whether or not the experienced fighter will be able to learn aiki is debatable. Aiki is in that sense ethically/spiritually neutral - it has no care of how you apply it. Want to beat someone to death with it? For good or evil, go ahead, it will let you! But aikido, such as it is, certainly has a philosophy behind when and how you apply it that is at odds with that and gives it a reason to exist beyond merely the study of aiki.
But now that the DR-aiki is making its way back to the masses, aikido, the modern organism, has a lot of thought and reflection to carry out as to whether that particular innovation should again be a part of the core identity of aikido - because it certainly is a fantastic tool to work with for enhancing the study of aikido - or whether aikido shall just remain an amorphous panacea ideology and/or a set of fantastical low-probability jujitsu overlaid with rolling gymnastics.