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You can call me William, Clifford.
Ok, William it is. :)
I feel at somewhat of a disadvantage not having as much scholarly knowledge about the Oz books. I only have the movie to go from, so bear that in mind when you read my responses.
I need to refer to one of my earlier suppositions about the 'why' - 1) Oz is an alternate reality of which Little Tib is a doorway. I prefer this explanation. I can best illustrate by answering your questions.
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Why doesn't Little Tib recognize any of the Oz characters?
Dorothy experienced the world of Oz in a dream state, but not necessarily 'dreamed' it. I think it is open to interpretation that she experienced an actual world called Oz through her dream. So, Little Tib being the extraordinary person he is, can not only visit Oz, but pull people out of it to help him out of tight spots. This is why he doesn't recognize the Oz characters - this is the world of the movie (or books), not our world! After all, Dorothy doesn't recognize them either!
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When is it taking place? Is it our near future, or an alternate history line?
Like I proposed above, I think this is the world of the movie in our near future (which would be about 100 years after Dorothy's world).
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Where is it taking place? It seems to be the United States, but why is the capital in Niagara? Has the US broken up?
Oh, probably in some vision of the world that Wolfe thought would be condusive to a ruthless form of citizen control. I think this is secondary detail without much depth behind it.
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Did Little Tib's parents really both become government agents?
I can't imagine his mother becoming an agent, and want to kill her child. I think it is likely that the father killed the mother. Pure supposition, though.
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Was Little Tib's father complicit in his blinding? Little Tib's first dream suggests this.
I don't have the book with me to re-read, but it never struck me that the parents were that imaginative.
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I don't think (1 (Tib as doorway idea)) is likely. Little Tib's contacts with Oz are either through dreams which are (to me at least) obviously dreams (albeit with many Oz elements) and not visits to an alternate reality (unless it is an alternate reality that is dream-like in a way that Oz, in Baum's hands at least, never was) or by interacting with a single Oz character in the "real" world. These Oz beings never talk about being transported from Oz in any manner, although they may mention Oz related people, places and things.
If dreams are the road to Oz, then Little Tib could be a 'lucid dreamer'. If his mind can bridge the gap without losing track of the 'real' world, then it stands to reason that he'd have a little more control than Dorothy. Here's some wild supposition - perhaps Oz is the source of mystical power, and that power spills over into our world in the form of psychic powers. Tib is the psychic embodiment of Oz's ruler, but doesn't know it yet. So, Tib can cross back and forth and bring people with him, including Oz characters who aren't surprised (he's the ruler, after all).
And the beings in the book never talk about being transported because they haven't been YET. Tib is in their future, too.
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(2 (Tib conjuring 'aquastors' of Oz characters)) fits in with the way I read the story much better. As to why the "spirits" Little Tib's "conjures" up take on the form of Oz characters, I still can't come up with a better answer than my suggestion in my Ozflash postings that the Oz images are coming from the mind of Little Tib's father, Big Tib. Of course this leads to another why. Perhaps part of Big Tib's (subconscious) mind is trying to offer Little Tib a safe hiding place or help and the best hiding place and source of help it can come up with is (childhood memories of) Oz.
I find your theory about Tib drawing from his father's subconscious mind to be very tenuous. Tib didn't seem that close to his father, and his father wasn't around for most of the story. Why not draw from any of the other characters? Why not his mother? His father doesn't seem preoccupied with Oz, so why would the characters be so important as to be conjured? (think about a hard drive - if a hard drive contains one MS Word file about Oz, what is the likelyhood that that one file would pop to the surface during a random search?). Tib's father doesn't seem too interested in saving Tib (didn't the Tin Man block a lethal blow?).
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It is interesting to compare Little Tib's angels with Silk's Enlightenment in TBotLS. The angels seems to help Little Tib, but it may well be that Little Tib is actually causing the helpful events to occur, with the angels as a guiding rather that effective force. Little Tib may be the help that was sent to him, as well.
I haven't read the Long Sun yet, but your statement 'causing the helpful events to happen' is exactly what I'm proposing, just drawing from a real source not a literary one.
So, what do you think? Fun topic!
cd