1. I understand that most (all?) good photographers shoot in manual mode. My photography class shot specifically in manual mode with our film cameras and so I am used to that. I have been shooting auto for the first few days of owning my D90, but I'm switching to manual soon once I get the hang of the basics of the camera.
I think your assumption that most good photographers shoot in manual is just wrong. It doesn't really give you much more control than the P, A and S modes, because in those modes you still have exposure compensation, and in P you have program shift.
What I'm curious about though... is it common to use auto focus, or is it still better to focus manually? I assume it depends on the situation?
The viewfinders in autofocus SLRs don't allow for easy, accurate manual focus. It's a big pain.
I might catch some flak for this, but I must say that I've always disliked autofocus SLRs, and DSLRs more so. I've always had problems getting them to focus on what I want, and with DSLRs, the viewfinders are typically tiny and dark. I'm so much happier with my Micro Four Thirds cameras than I've ever been with any autofocus SLR.
2. I have read about the option of using live view when taking pictures, but I haven't tried it. It seems I would have better control through the view finder. What are some opinions on live view?
Live view is great when your camera is on a tripod and you want extremely precise manual focus. Why? Because typically live view will give you an option to magnify the live image, and focus based on that. So for example, live view is definitely the way to go fo macro photography.
3. I shoot in color but usually convert to black and white with software. Should I use some sort of filter on my lens?
No. With B&W film, since the film cannot capture color, you control the translation from red, green and blue light into gray tones by putting color filters on the lens. With digital, the camera does capture color, so your control that when you convert the color image to black and white.