1. If a page is crawled by Google, it automatically gets into the index
(unless explicitly blocked by robots.txt).
False. The page can be crawled without being indexed. The page gets into the index except if it's not blocked by robots.txt or by meta robots noindex. On specific case I can't detail, a page only bocked by robots.txt can be indexed.
2. An indexed page always gets a ranking (high or low).
True except if website is penalized. In that case, the page can be deleted from the index by Google.
3. A page which is not referenced by any other pages, and which does not appear in a
sitemap, will never be crawled by Google, and will never get into the index.
True except if an internal or external link will point to this page in the future. Robots follow links...
4. Google will update its index and ranking for some sites faster than for others.
I'm not sure but I think true by logic.
5. More popular sites are indexed and ranked faster than less popular sites.
True. Trust websites are faster indexed and ranked than less trust websites. Indexation speed of a website also depends on number of links pointing to it.