As to point 1, it is more likely, from a practicing point of view, to know your geology and what clayey mineralogy comes from the parent rocks (if residual) or from "upland" rocks if lacustrine. You can get an idea by going the activity route.
Paul, a fellow Cornellian at the same time, is quite right - don't separate eo from Cc . . . in lab testing it is an easy process for one only has to plot strain vs log p' rather than e-log p'. In correlations it is a bit more difficult - which is why Lambe and Whitman's figure I alluded to can be used since it is actually a Cc/1+e0 correlation graph. Another way it to estimate eo by knowing the unit weight of the soil, its moisture content, (estimated) specific gravity (usually 2.65 to 2.7 is sufficient) and the phase volume relationships.
Critical state is not an easy subject to get into - as for "normal" practice, it has little application, in my view although Prof Graham (of University of Manitoba) and David Muir Wood and others might/will disagree. However, there are situations where there is no real clear choice as the normal ways just don't make sense. I suggest, as a start, to get either David Muir Woods book or the book by Malcolm Bolton (A Guide to Soil Mechanics) . . . I don't think I've ever used it . . . just has never been in vogue in practice (I started out in the mid-1970s; yes, I knew about it, but the engineering firm(s) I was with never considered it.
We can push the clients to survey buildings to build up a data base - but what clients are willing to do so? If you approach a client and ask him if you could do it (for free or if you can find a gov't agency to give you money to do so), I am sure most client's would be happy to do so. Hydrodams seem to love such instrumentation for the long term - but they have the dam safety boards to appease.
As for your last point - engineers who practice in a specific area do tend to develop their owns sense/feeling of what works and what serviceability movements will occur - it trumps for routine style jobs (one to 4 story commercial or residential buildings, storage tanks and the like) but I'd never bet on them on high profile/complex projects - - 1500 ft high rise or 60 ft deep excavations adjacent to existing buildings and the like.
Geotech practice is much more of a judgment practice than most other civil when it comes to behaviour as these "god given" materials do behave always like one wishes - what stability calcs for footings take into account varved clays, residual soil remnant joint planes, slickensides, etc. With COVs of 30 to 50% vs 3 to 5% for steel and concrete, there is little wonder that judgment is paramount and the structural types cannot understand why geotechs are so conservative. (of course, it is easier to retrofit a superstructure problem than a substructure one.