In regards to your first bullet, one of Parse's competitors, CloudMine, allows developers to write their own server-side JavaScript code that executes within a sandboxed environment: https://cloudmine.me/developer_zone#code/overview
Speaking as someone who has never used node.js before, it was nice to not have to worry about setup and just start coding.
http://www.crunchbase.com/company/cloudmine
CloudMine doesn't seem to have native mobile SDKs -- but that's actually the smallest piece of the puzzle.