If you want to set up clone or duplicate display instead of extended mode I suggest you using a screen resolution supported in common by both the built-in monitor and the external monitor/TV.
The laptop’s monitor supports 1366x768 but will not likely support 1920x1080. On the other hand the report indicates the TV does not list 1366x768 as a supported screen resolution, hence the recommendation above.
In regards of your second question, is the cable that you are using HDMI only or is it some type of adapter or converter?