1) Could the same SFML game code be used to compiled for android and ios, without platform-dependent changes required?
Yes and no. The API will be the same for both platforms, so you should just be able to use the same code, however since you're dealing with touch screens on mobile platforms and mouse/keyboard input on desktop platforms, you'll have to make sure your game and input design works for both systems.
2) I realise the support is experimental at the moment and maybe contains bugs, but could anyone make a tentative guess about when SFML will support mobile platforms in a stable manner? e.g. in a year's time could I release a professional standard stable game for android & iOS using SFML ?
We're currently lacking someone maintaining the iOS port, however development on the Android port, should probably get picked up pretty soon again.
But until we find someone stabilizing the iOS port, we can't give any kind of estimate unfortunately.