Is there a setting where I also when a HDMI cable is connected to show a live view on the camera display? 
No. There is no known way to do this, and it's likely not supported by the firmware.
Is there a setting where I can turn off the data transfer via USB so that the camera does not go into transfer mode and stays on?
What do you intend to use USB for, if you don't want the camera to go into transfer mode? Charging? If so, I'm not aware of a way to do that.
If you enable USB remote in "CHDK settings->Remote Parameters" and set the control mode to "None", the Canon firmware will ignore the USB connection completely. However, this will also mean it won't charge, so there would be little reason to connect USB.
You can use use script to call post_levent_to_ui(4482) to re-enable the display with USB connected, but (on my sx730 at least) this also makes charging stop. It's possible it still draws some power over USB, potentially extending battery.
Note that the camera behavior is somewhat different if it thinks it's connected to a dumb power supply vs a USB port on a computer. Some additional observations on charging behavior here:
https://chdk.setepontos.com/index.php?topic=13952.0
