Hi Feodor, that sounds good. I believe Azure static sites are nothing but a container called $web within the blob service. Hence, you should be able to use the standard Azure storage API (Powershell or API).
1) Yes, this would be great.
2) This turns out that it is not as important since using Azure Storage Static Webpages alone is VERY limitting and you very soon have to add the Azure CDN component that takes care of caching/compression.