You can think of ASVs as being 100% OTUs that have gone through some sort of denoising process. So instead of being operational taxonomic units clustered as some % threshold as a crude method for reducing noise by collapsing into clusters, they are amplicon sequence variants that recover true signal from the sample. I recommend this paper for a better idea of the transition from ASVs to OTUs.
Correct!
Same exact way as an OTU table. Both ASV and OTU tables are types of "feature tables" (feature being a generic term since this type of observation matrix can really contain all sorts of information). See the QIIME 2 tutorials for many examples of what one can do with a feature table.
Correct
Yes!
Good luck!