There's a high likelihood that beta savegames will not work with the full version. We're doing a lot of backwards compatibility stuff right now in the beta to bridge between different save systems and quest storage versions, etc. Some players are already experiencing that as slower loading times at the moment. The full version won't need to support that legacy stuff from the early beta and non-Special Edition stuff, so it might make the most sense for us to reset progress when the full game comes out... We'll see.
Yes, the online save system will work the same way it does now - letting you play the same Kingdom from anywhere that can run DD. You may have to do a couple of things to your Android and Steam versions to link to our save storage system, but once you've set it up it'll just work if it can find a net connection