Could you please refer me to the document that shows how to include fixed effect AND clustered standard error in SAS? I can't find any post that intuitively shows how to do it.
What you loosely describe could possibly be interpreted as a Generalized Estimating Equations model which can be fit in PROC GEE or PROC GENMOD. Another possibility, if the response is binary, is a conditional logistic model which can be fit using the STRATA statement in PROC LOGISTIC. You might want to look through the book "Fixed Effects Regression Methods for Longitudinal Data Using SAS" (Allison, P., SAS Institute, 2005).
ANOVA, or Analysis Of Variance, is used to compare the averages or means of two or more populations to better understand how they differ. Watch this tutorial for more.