I've been using the ActiveSync Remote Display that you can download free from MS - funny thing is, the link to it on the PowerToys page seems to be gone now for some reason.
I did find it in their Developer Power Toys page:
Just use ALT+PrtScrn and you have a snapshot.
As for the ring - check in Sounds (Start -> Settings -> Sounds & Notifications -> Notifications [at bottom])... there is a setting for Phone: Incoming Call. I believe it is linked to what you can select at (From the phone display -> Tools -> Options), but check both to make sure that you have a sound that will play, and that the Ring Type is not "None".
Only other thing I can think of to check is making sure sound is on at all - click the speaker icon at the top of the home screen - The system and phone volume levels are there, as well as an On/Vibrate/Off selection - I think this needs to be on even if you select Ring+Vibe from the phone menu.