It turns out that my main problem was I needed to copy files from my temp\deploy folder to my Azure container instead of files from my dist folder.
I also used an Azure CDN as described here, but I don't know if that was necessary.
Yes, you can use Azure virtual machine for SPFx development.
All you have to do is setup a SPFx development environment as explained in below documentation:
Set up your SharePoint Framework development environment
I think SPFx v 1.0 only supports node.js v 6.x.
This is the compatibility matrix:
Node.js LTS 6.x
Yeoman 2 (need to confirm)
Source: SPFx Development Environment Compatibility by HUGO BERNIER