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1) This is a function of your TV. If your TV supports picture-in-picture (PIP in your TV's manual) then you might be able to see TV channels in a window on top of the computer input.
2) The IR sensor on the NUC responds to the standard MCE remote controls. Windows Media Center, KODI (XBMC), and other media center software will respond to those IR codes
If you want your TV remote to control the NUC you will need CEC. In that case your TV remote controls your TV which then controls the NUC via CEC through the HDMI cable. The NUC's IR will only respond to MCE remotes and not to your TV's remote.