I think everyone starts off using their mouse first. I know I did too. I ended up switching to a wacom bamboo tablet because my hands kept getting sore from using it to draw. A few people here have already mentioned this too, but it also depends on what you're doing. Since I tend to do digital drawings/paintings and detailed illustrations, a tablet seemed like a better option for me.
Depends on what I'm doing. My tablet has been broken for my last several deviations (3d works) and it hasn't significantly effected their quality or process time. But (aside from vector work or pixel art) I'd never use a mouse for 2d illustration.
Depends on what you're getting. Something like this [link] (not that exact one of course, that's just an example from google.) They're amazing, having used them in the past, and much better than a normal usb wacom tablet like the one I use. Starting off a traditional artist it feels more like drawing on paper and I like to see the line being made by my pen, rather than feel it and looking at my monitor. Matter of opinion of course.
Bleh I tried playing with an ipad and their just not my thing. One of the main reasons I don't use Windows 8. I just don't like everything in that app layout, much less using/buying actual apps. Wacom + Windows 7 is the only way I prefer to go, but there is no way I'm throwing around that amount of money at the moment. My Bamboo Capture will hold me over for now. As long as it has at least 1024 pressure levels and 2500+ lpi I'm not complaining.
I like the Bamboo Fun, a friend of mine has one of those. I think most of the Bamboos are about the same. Only difference is some let you use your fingers and some don't I think? I'm not sure I haven't looked into any of the recent stuff. There is only one Wacom tablet I've encountered that I absolutely detested, can't remember what model it was though. That thing was HORRIBLE, like it couldn't handle anything I was trying to do with it. It was a few years ago though, so there is no telling.
Eh, that really depends on what the person is doing.
I use my tablet. But I use it for just about everything. I did draw with the mouse years and years ago.
You can do the same thing with a mouse, but it's more work. With a tablet, you can easily taper lines for instance, or control the opacity, just by the built in tools. With a mouse you can do that, too, but you use different tools and settings.
Mouse mostly if I loose my tablet pen, or if I draw in muro. Or for like my animations, I would live trace it, so I don't use much of a tablet.
An inspiration artist would be as a mouse user. When i mean mouse user, I mean mouse only, no tablet at all. I mean he tried the tablet, but he likes the mouse better. You can do amazing things with any tool if you got the patience for frustration and limitation. But if you don't, then using the tablet is fine.
Mostly for basic painting, you really only need the eye dropper (hold ctrl), and the small round brush. A mouse will force you to learn commands, so less time waisted.