1. How do you get on with your wheel?
Great, I buy it a drink now and then and we get on famously.
2. Do you generally do better or worse with a wheel than std controller?
Better, but see my next answer
3. Does it depend on the game you're playing at the time?
If the wheel support isn't done well or its super arcade-y I use a controller.
4. Do you find the some games are "more fun" to play with a controller than a wheel?
No game that supports a wheel properly.
5. Am I just bleating because I'm not used to using a wheel?
My standard response to the initial "wheelshock" most ppl suffer is "If your still getting bad times after using it as long as you have a controller then you have an issue."
6. Does it get better?
Ultimately I think a good wheel and pedal sets will give you better times, under certain conditions.
My recent experience with GT5 was that find every damn assist in the settings and turn it off (leave abs and traction to your liking). The seem to be put in place for pads not wheels and will make it harder for you.
Also if your striving to really drive your vehicle and turn all the assists off a wheel will help you do some much better than a wheel. If your racing under these conditions pretty much no one using a controller will be able to touch you.
Forcefeedback will help you feel the the car and your traction level and give you a greater awareness of the camber and contours of the road. The downside of forcefeedback is people ramming and nudging you, rumble strips and losing contact with the ground will affect your control of the vehicle in a way no pad will.
Speculating races run by ppl using wheels looks more natural and like real racing, its hard to explain but there is a real difference.
TL;DR Wheels kickass!
I do use a G27 however so YMMV.