Do you know how the government might acquire the data you're looking for? #3 is easy, #1 and #2 seem more in the domain of private surveyors that are more like pollsters and taking voluntary data sets to proxy the big picture. That has its own problems, of course.
There is already data collected on at least (2) and(3) of those points, although I can't tell you all of the details from memory, as far as who collects it, how it's collected, the frequency, etc. But I can clearly recall reading recent (and less recent) articles on economic issues that cited data reflecting underemployment, and wage growth.
There's a lot of interesting information here[1] regarding what employment related data is collected and reported by the BLS.
#3 is clearly happening in tech.