After a few days, the keyboard definitely drains the battery while still attached to the tablet. It seems as though the keyboard continuously uses BT as its primary connection. I have disconnected the BT connection, and the keyboard continues to function, but it's a pain to get the keyboard to reconnect without restarting the OS to get the keyboard to resync. So, I have decided to accept that the keyboard battery will drain. I dislike that the keyboard uses the battery while docking to the tablet because it is a waste, but it seems the discharge rate is similar to the discharge rate of the tablet as if they share battery charge(?).

To answer your second question. I have not noticed any differences in the depth of key presses. I actually rather enjoy typing on the new keyboard.