I think you're somewhat confused about the role of the original synthetic unity of apperception etc. in the argument. In figures in the argument mostly due to its descending nature. In the A-Deduction, Kant isn't very explicit about the fact that the assumption of the deduction is a prior unity. He thus establishes conditional claims and only later vindicates their antecedents (by positing further conditional claims, which finally are vindicated by assumption of the unity of apperception). Since he felt that this might lead to misunderstandings, in the B-Deduction he chose a different strategy, which instead begins from the unity. The labels "synthetic" and "original" are meant to point to the fact that the "analytic" unity assumed in each act of self-reflection is grounded in this synthetic, prior unity, i.e. this unity is the very possibility of self-reflection or, in Leibniz's and Kant's terminology, apperception. Kant is not concerned with any "primordial" or "ineffable" sense of self - quite the opposite, he tries to give precise and explicit meaning to the concept of having one's representations be theirs.
Furthermore, you seem to misunderstand what Kant refers to as the I think. I think is simply the general form of what is intuited, apperceived, through the inner sense (whereas the content is the sense, Sinn, as Frege also uses this term, of a proposition). That's why logical determinations, the categories, correspond to pure time-determinations, as you rightly note (5. Pure synthesis is combination of the manifold of time itself). The form of the inner sense is, afterall, time. This simply means that various forms of judgement, corresponding to the various categories, are represented through the inner sense as temporal relations. I cannot directly perceive temporal sucession (compare the 2nd Analogy where sequence of representations vs representation of sequence is discussed) - Kant agrees with Hume on this point - but when I reflect on my inference from A to B, I represent to myself the idea of B following A in time. This means considering the proposition which expresses this causal connection as an object (of the inner sense), as I think: p, instead of just p.
The I think must then be able to accompany each of our representations, but necessarily doesn't follow it in reality (which is what you seem to claim). Yet whenever I reflect on my cognitive operation, I represent them to myself as a "sense", "intension", "content" etc., i.e. as an object of the inner sense, as a certain structure which is interpreted temporally. This act of representing a certain proposition as an unified content is a necessary precondition of representing to oneself, e.g. temporal progression, since, as I have already said, it can't be directly perceived (but can be apperceived). This is where the qualitative and quantitative categories (and associated notions of number, degree etc.) become significant, as its the ability to represent to oneself the contents of one's perception as an unity, a sense, e.g. a number, makes possible apperception. This is why Kant defines number not only mathematically, but also procedurally: as product of successive (e.g. in time) acts of synthesis. And the product of a synthesis, in general, is not necessarily a concept, as you say, but an unity. As Gödel notes, Kant's notion of synthesis is related to the idea of taking a set of something in modern mathematics. A set, in Kant's terms, is a totality, e.g. an unity of a plurality. So your seventh remark (7. Pure concepts act as basis...) is correct, but is useless without the necessary elaboration.
I hope this clarifies and demystifies this complex topic a bit. I'd reccommend to focus less on Kant's specific terminology and think more about the general idea he tries to convey and how they relate to more modern notions. Keep in mind, though, that my discussion here was just a response to you on various points, not an exhaustive explanation of the Deduction.
