The finer details of semantic markup come down to personal opinion. Often semantic markup details are hotly debated. Commonly debated topics include:
The short answer is no - you should only have one h1 per document.
This will depend on the overall site in which the document sits. If you define your heading levels across a site, there many be times when a heading level is missing on a specific page, but to change it up or down a level may then take it out of context with the rest of the site.
There are two schools of thought on this. Some people believe that the site name is the most important information and should be wrapped in an h1 element. Others believe that the page title (which should match the document title) should be wrapped in the h1, and the site title sits above this with no real semantic meaning.