Audio is not likely to work, picture should be fine.

Posible, HDMI mandated some tv resolutions which the DVI device may not do - Also some HDMI devices get confused when they see the PC modes in the edid or whatever its called on DVI. Then you have the problems of no HDCP support.

To be sure get an active converter. I got one that also worked nicely to remove HDCP from a PS3 back when that was a problem for game capture devices.