When I try to register at Hapes Galactic Market or Centrepoint Marketplace, they both tell me my handle does not exist, or my character is dead or banned, neither of which are true. Any ideas?

You might need to contact the site owners about that as they should know the details of the web services they are using. Just be sure you are registering with your exact Combine handle and e-mail address.

Iirc, WebServices are still having problems after the server updates. Until they are fixed, best contact the market admins directly (emails should be on the sites).

What are the issues with web services?

They return no or faulty information, the following I got on IRC:

<Gawayne> odd thing is, i'm pulling the wsdl into my cache ...
<Gawayne> just nothing's returning on the function calls
<Gawayne> err, that's not entirely right
<Gawayne> it's returning something, but:
<Gawayne> Error: Response not of type text/xml