FYI, PageRank hasn't been updated since Dec. 2013, so for all intents and purposes it would be considered a 'dead' metric.
That's not to say that Google don't have a Pagerank 2.0 used to measure has authority, relevance and trust flow within an IA.
Also, please keep in mind that Page Authority and Domain Authority, as well as others metrics, are private, proprietary metrics and are merely observations on aggregated data: they are not official and simply a guide.
For these proprietary metrics, they are updated depending on the volume and volatility of the search times used. If your url ranks well for seasonal terms for example, the insights they provide are wrong or misleading. If you are a new website, it can also be completely mispleading.
Anyway, to answer your questions: