Yes, both Gnome and Sway have VNC: https://wiki.gnome.org/Projects/Mutter/RemoteDesktop, https://github.com/any1/wayvnc. Weston has RDP, and there are efforts being made to also add VNC.

I don't need VNC or RDP, so I don't know. I know that sharing other windows or my whole desktop in Google Hangouts doesn't work, but I rarely need that. I figure I'll log back in with an X session if I need that.