To switch between applications use either Shift-Menu and then subsequent presses of Menu, or Shift-Home to scroll through running applications.

The Tab key will move between fields and buttons on a form. When a form element has focus then pressing Space bar is equivalent to tapping on it.

To cycle through the tabs on the Home page, e.g. Applications, Settings, Files and any more you've created yourself, just press the Home button.

Hold down the Mail button to trigger a check for email. For some unknown reason this only seems to work is you have the Option->Show sync account on.