it is not necessary to do both — if you've read otherwise in our documentation, please tell us where so we can get that fixed 
Absolutely.
That normalization is not adequate for some analyses (e.g., alpha diversity comparisons require normalization for uneven sequencing depth between samples — currently we recommend rarefying to correct for that)
Any analysis in QIIME 2 (at least for "core" plugins) that requires normalization has that normalization built in — e.g., rarefying is performed automatically for alpha and beta diversity analyses. Rarefied tables should not be used for downstream analyses, e.g., that involve converting to relative abundance.
Did you have a particular step in mind?