Unfortunately not. We miss it too.

No, unfortunately not. I had the same problem a year ago when I installed the projector at my parents' house. But the good news is that there is a solution with an adapter. I'm not sure now, but I used either an HDMI to Ethernet adapter or a USB to Ethernet adapter. I think the former, but I'm no longer sure. It works absolutely fine with the adapter.

No

No, unfortunately not, only WiFi