Thanks for the report! I put it on my list of things that need looking at. You can expect a fix in the next patch, because this is a big issue for the touchscreen.
Not 100% sure if these will work, but as possible temporary workarounds:
(First problem) Convert the touch coordinates to the range of your current mode
(Keyboard problem) Before calling input, try setting the mode to 1280x720 and the view to 0, 0, 1280, 720, and change back after