More questions about estimating the fixed effects from GCTA-GREML

Two points of clarification on section 1 of gcta.freeforums.net/thread/211/estimating-fixed-effects-gcta-greml

1. Categorical covariate (e.g. sex and cohort): --covar option
If the covariate is a categorical covariate, there will be t - 1 variables (where t is the number of categories, e.g. t = 2 for sex) because otherwise the X^TV^-1X will not be invertible (X is design matrix for the fixed effects and V is the covariance-covariance matrix). Therefore, the model is
y = mu + x_c(2)*b_c(2) + x_c(2)*b_c(2) + ... + x_c(t)*b_c(t) + g + e

1. The underlined portion above should in fact be  x_c(3)*b_c(3), correct? Category 1 is left out from this analysis, because it would make the X^TV^-1X matrix not invertible. 

2. The mu above is in fact the mean of just the individuals for whom x_c(1) = 1, correct? Perhaps mu_c(1) would be better notation.

From this, does V_p (as reported by GCTA) equal the variance of (y - [mu + x_c(2)*b_c(2) + x_c(3)*b_c(3) + ... + x_c(t)*b_c(t)])? If so, how many degrees of freedom are used in computing the variance (assuming there are N individuals)?