is it illegal to buy a second hand bike in China as some web pages have said.
You can't change the name of registration, this is because the cops want an easy job, but I doubt it's illegal. As far as we know a bill of sale is an agreement of change of ownership. But who knows? This is China

Can I buy an XL or XR 650 Honda in China? Is it made here or in Japan and imported?
They don't make XL or XR 650's here yet, but actually they make some similar bikes such as the Jialing 600. If you wanted a Honda you'd need to buy one that would have plates if it had been legally imported or without plates if it had been illegally imported from Hong Kong. Although you'd be very lucky to find one. (hens teeth)

What provinces allow bikes that big to be registered? Hainan is only 250.
You'll find that that is probably wrong and that you can get something bigger than 250 registered in Hainan, but it's very uncommon. Many other provinces will allow a bigger bike to be registered with a ton of money and paperwork if it's been imported officially or a Chinese made bigger bike you can hassle the dealer/factory to register it before you give them any $$$. The process then becomes much simpler

What cities can I not ride a bike through?
Little bits of lots of cities. Most of some.

Beijing, Shanghai, Guangzhou etc. Bigger city usually equals more restrictions.

Caution cynical rant ahead ...............

The culture here is that cars are just plain wonderful in every way, they give you status keep you dry in the rain cool in the summer and warm in the winter. You can transport your family and friends around and generally impress everyone. So who would want a bike? Bikes? They get in the way of our car and if it goes faster than a Volkswagen Santana that must be dangerous and annoying, plus people who are poorer usually ride bikes. So we should find a way to legislate them off the road despite the fact that they hardly use up any road-space and use far less fuel than a car.

There are no Honda shops in China so where would I find a Honda?
There are Honda dealerships but they are all joint-ventures with Wuyang or Sundiro and they only make small bikes up to 150cc. You'd need to find something imported.

Some people say you can buy a bike but not a plate. What about that?
Some areas are restrictive on registrations for bikes some unofficially imported bikes from HK can't be registered, and some people who live in the countryside don't care about paying for registration or insurance.