C2 can work very well on mobile.
If you use a TextBox field, then the mobile will automatically call up an on screen keyboard.
If you use Buttons, touch works as expected.
and you can manually build any interface you can imagine.
you can also access many mobile specific features - like the camera, microphone, tilt sensors...
if you want to try a project I use to test things out on my phone, use your phone's browser to go to: http://www.rieperts.com/games/buttons
you can pinch to zoom, and pan around when zoomed in. You can drag the button panel around. Some of the buttons are toggle buttons, and some are push buttons... some buttons to more than one thing, and it does change occasionally when I am testing something new.
you can also try http://www.rieperts.com/games/birds
which is an angry bird clone I did as a test too.
Mobile C2 games/apps that you host yourself run better if you have the user save the game to their Home Screen - then you don't get the browser menus at the top and bottom of the screen getting in the way.
You can also export your game to various mobile wrappers and upload them to app stores.