Multiple Comparison Correction - Help needed !

#1
I know the concept that one should have statistical correction if multiple comparison are made between means. Such as the well-known bonferroni correction.
Now i did ANOVA with post hoc tests using Dunnett's T3 test - My question is - Does or Does it not include correction inside the test for the multiple comparison. If not, a thing which looks not so smart to me as a default, How do i create ANOVA post hoc test with the correction assuming the variances Are NOT equal.

Thanks !!! I really need an answer to this !