To avoid reinventing the wheel, below is some existing quality material on socionics. The quality of socionics information online is uneven, so here are some links that are of high quality and which have contributed to my own understanding. Disclaimer: I don't necessarily agree with all of the information provided but it is overall very good.
Socionics as a Potential Scientific Theory This is sort of what I have been aiming to do with socionics: make sure that it is firmly grounded on everyday concepts (rather than abstract and ill-motivated ones), and ideally also with self-evident axioms that the rest of the theory can be derived from. This means closely examining actual human interaction and how it plays out. In fact, relationships are purely secondary to this in my view: the relationships between types are a result of information metabolism (plus type-related worldviews) rather than the other way around. The latter has historically been poorly elaborated in socionics. For any interaction (in real life, or a relatively spontaneous dialog which has been recorded on video) it should be possible to completely dissect the information metabolism that is going on. (The interaction between elements does not even necessarily occur between two different types; it is also a process that happens within the mind, or abstractly, as a consequence of making decisions.)
The Socionics Community I'm happy to say that the English-speaking community (however small it may be) has definitely made real progress, with people proposing original hypotheses and definitions. Real synergy has been a somewhat more elusive goal, though I have definitely benefited from other community members' insights.
The Socion, part 2 Here Augusta explains some of the fundamental concepts of socionics. Many socionists would do well to emulate her approach: "There isn't a drop here of 'pure theory' that doesn't come out of our observations." Her descriptions of IM elements contain minor inaccuracies but they remain among the best to this day.
The Dual Nature of Man Augusta's seminal work. The full translation can be found elsewhere, but the initial part is the most important. (Augusta devotes considerable space to elaborating type dichotomy traits and duality descriptions, neither of which are conceptually central to socionics in my view.)
The Semantics of the Information Elements This is good for getting a more detailed description of each IM element.
Bukalov and Karpenko interview about the history and development of socionics
The Dual Nature of Man, machine translated a rough translation of the whole work
Filatova portraits (I do NOT endorse using visual identification to type people, except as described by Rick DeLong at the above link. However, these portraits are interesting nonetheless.)
Model A: Blocks and Functions of the Socionic Model of the Psyche A more detailed treatment of functions and their categories. In my opinion, some of these dichotomy descriptions are inaccurate and need to be reformulated, if they are meaningful at all.
My Personal Typology some other important factors to consider when analyzing personality
The Reinin Dichotomies are Dead I actually do think there is potential in certain Reinin dichotomies (in particular the ones that correspond to groups of relationships, such as Process/Result, Positivist/Negativist, and Static/Dynamic) — but they 1) require new interpretations and 2) should be considered as a byproduct of the functional ordering. The standalone traits as classically described are not very useful for typing and in fact can often be positively misleading. For example, I would not rule out someone being a Declaring type just because they ask a lot of questions.