I think the baseline toolkit could be the same, with some extra components for different form factors.
We're working on something like that (multi form factor UI toolkit) for Ubuntu, with Qt. Will see how far it goes.
No! No they absolutely don't!
Almost every Android app is clearly design for use on a touch device. Every aspect of the design is intended to be touch-first. That's totally fine – but the fact that they can be used with a mouse on a desktop does not mean that they work pretty well. The user interface paradigms are really very different.