1) Yes, now it's possible with some tips and optimizations. (There's a tutorial about mobile devices. The author has some apps on google play).
Directcanvas and cocoonjs will remove this bottleneck.
2) In my case (I'm on the android side) I use 800x480 resolution and looks good on different devices.
3) Currently I use phonegap (getting 15-20 FPS) but I'm waiting for CocoonJS release. I used AppMobi containers for a while but I found it somewhat bloated and I really don't like the unkind support.
4) Yes. You can use webstorage plugin. It works with phonegap. Hopefully there will be something similar in CocoonJS (CocoonJS doesn't use a browser so webstorage plugin support is still a question mark)