1) Yes and no. It does autotune, but not VOR stations (only DME), and you would usually not even notice. The nav panel on the NG does not have a manual/auto selector like on the classics since the FMS can autotune the two DMEs directly and independently from the manually selected station. You can see which stations it is interrogating on the NAV STATUS page on the CDU. The automatically tuned DME returns are supressed and not displayed on the ND (only whatever you tuned manually)
2) This is a software option on the real airplane, some airlines have the green dotted line, some don't. Get the PMDG, as far as I know you can select whether you want it or not there
3) I guess that has been answered - no way to select VOR autotuning, so thats it.