1. The screen is fixed in its button positions and sizes at 3x4 spaces. So you could do 2x2 if you had to, but it would simply involve leaving the other buttons empty (and lop sided)! :-)

2. Yes (they're shown on the same buttons so have the same character restrictions).

3. They're fully programmable like other URC remotes. The "LIGHT" button can be used to specifically turn the remote on.

4. Although the screen is larger I suspect that the increased power draw is minimal over URC's other LCD models. However, using the larger backlight would probably drain things quicker (sorry, I don't have a TX-1000 to confirm). And no, the TX-1000 and MX-900 don't have rechargable battery capabilities (although there's nothing to stop you from using your own NiMH cells...)