We also have a small dog and live in Southern California near bobcats and coyotes. I don't let him outside alone because of that, but I will definitely keep a closer eye on him when I hear the crows. Maybe listening for the crows will also help me to get some better photos of the bobcats. I'm often a bit too late with my camera by the time I spot one.
(1) If my neighbor complained about the American Crows killing songbird nestlings, I would inform my neighbor that although the American Crows kill some songbird nestlings, the majority of the killing of songbird nestlings is done by squirrels, chipmunks, and snakes, and that crows kill far less songbird nestlings than some other birds and small to medium mammals.
(2/3) I used to live near Toronto in Ontario, Canada. There I often saw the American Crow, and I don't recall seeing the Common Raven. I now live in Southern California and I see both the American Crow and the Common Raven most days. I have not seen a nest for either. One of the main differences I see is that when I see American Crows they are usually in a group. I may notice only one at first, but once I look around I usually see several more nearby. With the Common Ravens I usually see them in pairs, often appearing to be playing in the wind as they soar around overhead together. I often go to Torrey Pines State Reserve, where you are almost guaranteed to see at least one pair of Common Ravens.