What conditions should be fulfilled for Fry to be a good approximation of mroast with infinite rotations? The manual says that the df.prior should be large and set.statistic="mean". What determines the prior degree of freedom of residual variance? I am guessing it is the number of replicates per experimental conditions. Thank you.

df.prior is determined by the heterogeneity of variances between genes. It has nothing to do with the number of replicates.

You can examine df.prior for your data by:

fit <- lmFit(y, design)
fit <- eBayes(fit)
fit$df.prior

or

fit <- eBayes(fit, robust=TRUE)
summary(fit$df.prior)