You can't set up the MacBook to automatically switch off the screen. The best you can do is to close the lid to put it in clamshell mode. It'll go to sleep and you'll have to wake it up - using the remote should do that.
As for the resolution, when you connect to the LCD TV, the MacBook will output to it in the correct resolution. The list of resolutions in system preferences is those the MacBook's own screen supports, not the resolutions it can support externally.