(1)Would you know how to obtain model standard deviations and model autocorrelations of endogenous variables after bayesian estimation.
Ie,Does “oo_.PosteriorTheoreticalMoments.dsge.covariance.Variance.y.y” deliver the variance of y?

(2) Also, would “oo_.PosteriorTheoreticalMoments.dsge.correlation.mean.y” deliver the model implied autocorrelation of the variable y?

The fields of oo_.PosteriorTheoreticalMoments.dsge
denote the moments you are looking at. The next field provides the statistic for that moment considered.

oo_.PosteriorTheoreticalMoments.dsge.covariance.Mean.y.y should be the mean covariance between y and y, i.e. the variance. What you wanted to look at is the variance of the covariance over the MCMC draws.

The autocorrelation of y, starting from lag 1, should be in oo_.PosteriorTheoreticalMoments.dsge.correlation.Mean.y.y
If you want contemporaneous correlations, you need to use the unstable version with the

option and then look at e.g. oo_.PosteriorTheoreticalMoments.dsge.contemporeaneous_correlation.Mean.y.c
to get the correlation between y and c