I will try to provide brief answers, and I remain at your diposal in you are interested in further specifics
Measuring human capital: so far I have used mainly educational statistics (enrollment rates, graduation rates, educational attainment, etc.)
Measuring its impact on the macroeconomic output: using 1) human capital economic growth models - both neo-classical and endogenous; 2) time series analysis (ECM, Granger causality)
What is the use of finding it out during the past regime rather than the current government?: Firstly, the impact of human capital on economic develment is observed over long periods. Current human capital stocks within the active population have been accumulated over the last 60 decades. Furthermore, transition economies inherited human capital from the past regime. So, economic growth during the transition is determined by human capital accumulation during communism in addition to the impact of all other factors.